Ultra-high-energy cosmic rays (UHECRs) represent the most energetic particles ever observed in nature, with energies exceeding 10¹⁸ eV and extending up to about 10²⁰ eV. These particles, primarily protons and atomic nuclei, arrive at Earth carrying energies far beyond those achievable in terrestrial accelerators such as the CERN [1]. Their origin, acceleration mechanisms, and propagation through the universe remain among the most compelling open questions in modern astrophysics and astroparticle physics [2][3]. The study of cosmic rays dates back to the early 20th century, but the existence of UHECRs was firmly established through extensive air shower observations. When these extremely energetic particles interact with Earth’s atmosphere, they produce cascades of secondary particles that can be detected using large-scale observatories. Leading facilities such as the Pierre Auger Observatory in Argentina and the Telescope Array Project in the United States have significantly advanced our understanding of the UHECR energy spectrum, mass composition, and arrival direction distribution [4][5]. These experiments have revealed key spectral features, including the “ankle” around 10^18.7 eV and a suppression at the highest energies, commonly interpreted as a consequence of interactions with the cosmic microwave background (CMB) through the Greisen Zatsepin Kuzmin cutoff [6].

One of the central challenges in UHECR research lies in identifying their astrophysical sources. Due to deflections in galactic and extragalactic magnetic fields, the arrival directions of charged cosmic rays do not directly point back to their origins, complicating source identification. Nevertheless, theoretical considerations impose constraints on potential sources through the Hillas criterion, which relates the maximum attainable energy of a particle to the size and magnetic field strength of the acceleration region [7]. This criterion narrows down viable candidates to extreme astrophysical environments such as active galactic nuclei, gamma-ray bursts, and rapidly rotating neutron stars. In recent years, the field has entered a new era driven by the emergence of multi-messenger astronomy, combining observations of cosmic rays, neutrinos, and gamma rays. This approach has opened new pathways for probing the origin of UHECRs and testing source models [8]. Despite these advances, several fundamental questions remain unresolved, including the precise composition of UHECRs at the highest energies, the nature of their sources, and the mechanisms responsible for their acceleration.

Ultra high energy cosmic rays (UHECRs) exhibit a set of distinctive observational properties that provide essential clues about their origin, composition, and propagation through the universe. One of the most important characteristics is their energy spectrum, which follows an approximate power-law behavior over many orders of magnitude in energy. However, this spectrum is not featureless; it displays notable structures such as the “ankle” around 10^18.7 eV, where the spectral index hardens, and a suppression at energies above ~5 × 10¹⁹ eV [2][4]. This high-energy suppression is widely interpreted as a consequence of interactions between UHECRs and photons of the cosmic microwave background (CMB), leading to energy losses through processes such as photo-pion production and electronpositron pair production, commonly described by the Greisen-Zatsepin-Kuzmin cutoff [6]. Observations from major experiments like the Pierre Auger Observatory and the Telescope Array Project have confirmed these spectral features with increasing precision [9][10].

The mass composition of UHECRs is another important characteristic that is currently being studied intensely. Unlike energy, which can be directly estimated through observation of UHECR cascades, mass composition cannot be determined by measurement and needs to be deduced from observables in air showers, such as the depth of shower maximum (X_max) and its fluctuations. These parameters are known through experimental observation, but the interpretation of the latter in terms of the mass of the primary particle relies heavily on the theoretical model of interactions between hadrons, which is extrapolated to the energy region not achievable by any accelerator on Earth. The data from the Pierre Auger Observatory indicate a gradual change in the primary composition of particles from lighter to heavier, while results obtained by the Telescope Array Project are also consistent with the light composition of particles [10][11].

Figure 1 shows the evolution of the mass composition of the ultra-high-energy cosmic ray (UHECR) energy spectrum is inextricably coupled with its interpretation. The top panel emphasizes the all-particle cosmic ray flux, which has been scaled by E³ to emphasize spectral features. This illustrates a high degree of agreement between the Telescope Array (TA) and Pierre Auger Observatory across the ankle region, as well as an empirical multi-component fit. The shifting mass composition illustrated in the subsequent panels can be used to physically interpret the structural characteristics of the spectrum, particularly the suppression at the highest energies (~10^19.5 eV). By the depth of atmospheric shower maximum (X_max), air shower longitudinal profiles offer the most reliable experimental proxies for primary mass identification. At lower energies (~10^18.0 eV), the mean depth <X_max> closely aligns with light, proton-like predictions. However, it transitions to the heavier, intermediate-mass bands at higher energies, as illustrated in the middle panel. This trend is further supported by the shower-to-shower fluctuations, RMS (X_max), which are depicted in the bottom panel. As the energy increases toward 10^19.5 eV, the standard deviation of the depth maximum decreases significantly from ~55 g/cm² to less than 30 g/cm². In comparison to primary protons, heavy nuclei exhibit inherently smaller stochastic fluctuations due to their larger cross-sections and tendency to fragment early in the atmosphere. These observables, when considered collectively, strongly suggest a composition transition from light, proton-dominated primaries to a mixed, increasingly heavy composition beyond the ankle. This transition provides essential constraints for UHECR acceleration and propagation models [12].

UHECR arrival directions become a valuable tool in determining the source of UHECRs. Lower energy cosmic rays have nearly isotropic arrival directions because of deflections by galactic magnetic fields. However, at higher energies, deflections by magnetic fields are weak enough to reveal anisotropy at a large scale. An interesting result from the Pierre Auger Observatory was the detection of a dipole anisotropy above 10¹⁸ eV [13]. A hotspot in the northern part of the sky has been found by the Telescope Array Project; however, the statistical significance and physical meaning of the findings are still being studied. The findings concerning large-scale anisotropies give information about the sources; nevertheless, they should not be considered as connections to the objects themselves [14]. Finally, the propagation of UHECRs through intergalactic space significantly influences their observed properties. During their journey, these particles interact with background radiation fields, including the CMB and extragalactic background light (EBL), leading to energy attenuation and modification of the energy spectrum. Moreover, deflections in galactic and extragalactic magnetic fields obscure the direct correlation between observed arrival directions and source locations. These propagation effects, combined with uncertainties in source distribution and composition, make the interpretation of UHECR observations a complex but deeply informative puzzle [2][6].

Figure 1. UHECR energy spectrum and mass composition observables from the Telescope Array (TA) and Pierre Auger Observatory. Energy spectrum scaled by E³, shown with a multi-component elemental fit (H to Fe). Mean depth of shower maximum, <X_max>, as a function of primary energy. Shower-to-shower fluctuations, RMS (X_max), vs. energy. Middle and bottom panel data are contrasted against pure proton (red curves) and pure iron (blue curves) simulations across multiple hadronic interaction models [12].

The Hillas criterion offers the necessary condition for the acceleration of UHECRs since the requirement for the condition implies the presence of confinement of the particle inside the region of acceleration. However, meeting the Hillas criterion is not enough to conclude about the viability of the possible source. The accelerator should not only meet the condition but also be able to accelerate particles up to the necessary energy within the period of the available acceleration time, as well as escape from the acceleration region before the change occurs within the source environment. Also, energy losses due to synchrotron radiation, photohadronic interactions, pair production, and adiabatic expansion can limit the maximal attainable energy. In a more general sense, the highest possible energy which can be reached through an astrophysical accelerator depends on the trade-off between the time scale for acceleration and that of losses, escape, and dynamics. Consequently, the Hillas diagram may be considered as a means of initial screening rather than being a way of unambiguously identifying the sources of UHECRs. If the sources meet the Hillas criterion, they have to be subjected to the tests involving acceleration and propagation [7].

Figure 2. Hillas diagram of magnetic fields versus size of candidate UHECR sources. Above the diagonal lines protons or iron nuclei (as labelled) can be confined to a maximum energy of Emax = 1020 eV. The most powerful candidate sources are shown with the uncertainties in their parameters [17].

One of the most widely studied mechanisms is Fermi acceleration, originally proposed by Enrico Fermi. In its first-order form, also known as diffusive shock acceleration, charged particles gain energy through repeated crossings of shock fronts in astrophysical plasmas. Each crossing results in a systematic energy gain proportional to the velocity difference across the shock, leading to a power-law energy spectrum consistent with observations of cosmic rays [15][16]. This process is particularly efficient in environments such as supernova remnants, relativistic jets of active galactic nuclei, and gamma-ray burst outflows. Second-order Fermi acceleration, involving stochastic interactions with moving magnetic irregularities, also contributes to particle energization, although it is generally less efficient due to its dependence on the square of the velocity fluctuations [15]. Figure 2 shows the Hillas Diagram for Ultra-High-Energy Cosmic Ray (UHECR) Sources. The plot illustrates the magnetic field strength versus the characteristic size for various potential astrophysical accelerators. The solid diagonal lines represent the theoretical minimum constraints (the Hillas criterion, B × R ≥ E/Zec) required to magnetically confine and accelerate a protonand an Iron nucleus ( Fe , lower line) to an ultimate energy of 10²⁰ eV. Candidate sources lying above or intersecting these linessuch as Active Galactic Nuclei (AGN), AGN jets/hotspots, Gamma-Ray Bursts (GRBs), and Intergalactic Medium (IGM) shocksare theoretically capable of producing UHECRs, whereas objects below the lines, such as Galactic Supernova Remnants (SNRs), lack the necessary confinement capabilities [17].

Another important mechanism is magnetic reconnection, in which oppositely directed magnetic field lines rearrange and release stored magnetic energy into kinetic energy of charged particles. This process can occur in highly magnetized and turbulent environments such as pulsar wind nebulae, magnetospheres of neutron stars, and relativistic jets. Magnetic reconnection has been proposed as a rapid and efficient acceleration mechanism capable of producing non-thermal particle distributions and potentially contributing to UHECR production, particularly in compact sources with strong magnetic fields [18]. In addition to these mechanisms, shear acceleration and unipolar induction have also been explored in the context of UHECR origin. Shear acceleration occurs in regions with strong velocity gradients, such as the boundaries of relativistic jets, where particles gain energy through repeated scattering across layers of different flow velocities [19]. Unipolar induction, on the other hand, is associated with rapidly rotating neutron stars or magnetars, where enormous electric potentials are generated due to rotation in the presence of intense magnetic fields. These systems can, in principle, accelerate charged particles to ultra-high energies over very short timescales [20]. Despite the variety of proposed mechanisms, achieving the highest observed energies remains challenging. Efficient acceleration requires not only strong magnetic fields and large spatial scales but also sufficiently long confinement times to allow particles to gain energy before escaping the acceleration region. Energy losses due to radiation and interactions with ambient matter and radiation fields further constrain the efficiency of these processes. Consequently, identifying the dominant acceleration mechanism for UHECRs likely requires a combination of theoretical modeling and multi-messenger observational evidence [7][16]. The various acceleration mechanisms postulated to explain the acceleration of UHECRs are explained in Figure 3. They involve the various processes by which particles could be energized in an astrophysical setting, which include diffusive shock acceleration, magnetic reconnection, shear acceleration, and unipolar induction.

Figure 3. Schematic illustrations of the principal acceleration mechanisms proposed for ultra-high-energy cosmic rays (UHECRs): (a) diffusive shock acceleration, (b) magnetic reconnection, (c) shear acceleration, and (d) unipolar induction in rapidly rotating compact objects. These mechanisms operate in extreme astrophysical environments and provide potential pathways for accelerating charged particles to ultra-high energies.

Even though several candidate source classes meet the Hillas confinement criterion, the mere fulfillment of the condition cannot prove their ability to accelerate particles up to the energies of the detected ultra-high-energy cosmic rays. Particle acceleration time needs to be short enough relative to both escape and evolution timescales, and radiative, interaction, and adiabatic energy losses have to be small enough for the particles to be able to achieve ultra-high energies. Each type of sources has different restrictions regarding these criteria. For example, compact objects can generate very powerful magnetic fields, but they may experience strong radiative losses, and transient sources, like gamma-ray bursts, have to comply with very strict acceleration, escape, and event rates criteria. On the other hand, extended systems like galaxy clusters can offer a large volume of confinements, but their magnetic fields may be comparatively weak, and their acceleration time may be long. Among the most widely discussed candidates are active galactic nuclei (AGN), which host supermassive black holes at their centers and often exhibit powerful relativistic jets. These jets, extending over kiloparsec to megaparsec scales, provide ideal conditions for particle acceleration via shock acceleration and magnetic turbulence. Centaurus A and other radio galaxies have been suggested as the sources of UHECRs owing to their closeness to Earth and their correlation with UHECR directions, but these correlations do not make for definite source identification yet [2][21]. The large-scale structure and magnetic field strengths in AGN jets and lobes make them strong candidates for accelerating particles up to the highest observed energies.

Another prominent class of sources is gamma-ray bursts (GRBs), which are among the most energetic transient events in the universe. GRBs are characterized by ultra-relativistic outflows and internal shocks capable of accelerating particles through first-order Fermi processes. The short duration and immenserelease in GRBs make them attractive candidates for UHECR production, particularly in models where protons are accelerated in the relativistic fireball and subsequently escape into intergalactic space [22]. However, the lack of strong correlations between UHECR arrival directions and observed GRB events has raised questions about their dominant contribution. Starburst galaxies have also emerged as promising candidates due to their high rates of star formation and supernova explosions, which generate strong galactic winds and turbulent magnetic fields. These conditions can sustain efficient cosmic ray acceleration and confinement. Correlations have been found between the directions of arrival of UHECRs and nearby starburst galaxies by the Pierre Auger Observatory, indicating their possible role in making up the flux; nevertheless, the correlations do not imply that each starburst galaxy is definitely a source of UHECRs [1].

Compact objects such as magnetars and rapidly rotating neutron stars are also considered potential sources of UHECRs. Magnetars, with surface magnetic fields on the order of 10¹⁴ - 10¹⁵ G, can generate enormous electric potentials capable of accelerating charged particles to ultra-high energies through unipolar induction. Similarly, young pulsars with rapid rotation rates may provide the necessary conditions for particle acceleration, although energy losses and escape mechanisms remain important considerations [20]. On even larger scales, galaxy clusters and large-scale structure shocks have been proposed as possible acceleration sites. These environments contain vast reservoirs of hot plasma and extended shock fronts formed during structure formation processes. Although the magnetic fields in these regions are relatively weak, their large spatial extent may compensate, allowing particles to reach high energies over long timescales [23]. However, achieving the highest observed energies within realistic time constraints remains a challenge for such models. In addition to conventional astrophysical sources, more speculative or exotic scenarios have been proposed, including the decay or annihilation of super-heavy dark matter particles and the presence of topological defects formed in the early universe. These models aim to explain UHECRs without requiring extreme acceleration processes, instead attributing their origin to the release of energy from fundamental physics phenomena [24]. While intriguing, such scenarios currently lack strong observational support compared to astrophysical acceleration models.

Overall, while several candidate sources satisfy the basic physical requirements for UHECR acceleration, no single class of objects has been conclusively identified as the dominant contributor. It is likely that multiple source populations contribute to the observed UHECR flux, with their relative importance depending on energy, composition, and distance. Continued progress in multi-messenger observations and high-precision anisotropy studies will be crucial for resolving this long-standing mystery. Each of the classes of possible candidate sources faces its own physical constraints even if it fulfills all the essential confinement conditions. AGNs have big acceleration zones and powerful magnetic fields, however, acceleration and escape of particles in relativistic jets are limited by the time scale and energy loss conditions. GRBs have a great advantage in terms of powerful relativistic outflows; however, being transient events limits event rates, acceleration timescales, and particle escape from them. Magnetars as compact objects can produce extreme magnetic fields and fast acceleration of particles; however, powerful radiative losses and interactions can put a limit on achievable energies. The most favorable candidate sources for UHECRs can be starburst galaxies since they provide effective confinement and constant activity, but the maximal acceleration energies can be limited by the parameters of their galactic environment.

Once accelerated at their sources, ultra-high-energy cosmic rays (UHECRs) embark on long and turbulent journeys across the cosmos, during which their energies, trajectories, and even identities can be significantly altered. The propagation of UHECRs is governed primarily by their interactions with background radiation fields and by deflections in cosmic magnetic fields. These effects collectively shape the observed energy spectrum, arrival directions, and composition at Earth, turning the universe into a vast, diffusive labyrinth rather than a straight highway from source to detector. A dominant factor influencing UHECR propagation is their interaction with pervasive photon backgrounds, particularly the cosmic microwave background (CMB) and the extragalactic background light (EBL). High-energy protons interacting with CMB photons undergo processes such as photo-pion production, leading to substantial energy losses above ~5 × 10¹⁹ eV. The above phenomenon can be summarized by what is known as the Greisen-Zatsepin-Kuzmin cutoff, which places a limit to how far the most energetic cosmic rays will travel based on their energy. The extent of this cutoff will depend on the energy and charge of the particles and the interactions that take place with the photons; hence 100 Mpc should not be considered a universal limit [2][6]. For heavier nuclei, photodisintegration becomes the dominant energy loss mechanism, where interactions with background photons cause nuclei to fragment into lighter elements, altering the observed mass composition during propagation [25].

In addition to energy losses, UHECRs experience deflections due to galactic and extragalactic magnetic fields. Although these fields are typically weak (ranging from nanogauss in intergalactic space to microgauss within galaxies), their cumulative effect over cosmological distances can significantly bend the trajectories of charged particles. The magnitude of deflection depends on the particle’s rigidity (energy divided by charge), with heavier nuclei experiencing larger deviations. As a result, even the most energetic cosmic rays may arrive at Earth with directions that only loosely correlate with their sources, complicating source identification efforts [3]. Another important element of the propagation of UHECRs is the generation of secondaries, which is the foundation of multi-messenger astrophysics. The interaction of UHECRs with background photons creates high-energy neutrinos and gamma rays via mechanisms such as pion creation and decay. Neutrinos travel essentially unscattered through cosmic magnetic fields and can travel across cosmological distances without significant absorption; however, high energy gamma rays may be absorbed by interactions with background radiation fields. Thus, the secondary messengers provide a complementary view of UHECR source environments. Neutrino observations made with observatories such as IceCube Neutrino Observatory provide key constraints on the modeling of the sources and propagation of UHECRs, but the observations are not yet enough to detect a conclusive population of UHECR sources [26]. Figure 4 compares the simulated ultra-high-energy cosmic ray (UHECR) energy spectra obtained for four different source composition models (Models A-D). In each panel, the total predicted spectrum (gray curve) is decomposed into the contributions from individual nuclear mass groups, including protons, helium, light nuclei, intermediate-mass nuclei, heavy nuclei and very heavy nuclei. The blue data points represent the measurements from the Pierre Auger Observatory, providing a benchmark for comparison. All models assume identical propagation conditions, with a source density of 1.4 × 10⁻³ Mpc⁻³, an extragalactic magnetic field strength of 1 nG, the JF12 + Planck Galactic magnetic field model, and a coherence length of 200 pc. Although each model adopts a different elemental composition at injection, they reproduce the observed UHECR spectrum with varying relative contributions from different nuclear species. The figure demonstrates that the high-energy suppression and the overall spectral shape are strongly influenced by the source composition and propagation effects, highlighting the importance of composition-sensitive measurements for constraining the origin and acceleration mechanisms of UHECRs [27].

The combined effects of energy losses, magnetic deflections, and nuclear interactions lead to the formation of a so-called cosmic ray horizon, beyond which UHECRs cannot reach Earth with their original energies. This horizon depends on both energy and composition, with higher-energy particles originating from relatively nearby extragalactic sources. Consequently, the observed UHECR flux carries imprints of the local large-scale structure of the universe, including the distribution of galaxies and galaxy clusters [2][25]. Despite significant theoretical and observational progresses modeling UHECR propagation remains challenging due to uncertainties in the strength and structure of extragalactic magnetic fields as well as the poorly constrained intensity of background radiation fields. Numerical simulations incorporating realistic source distributions and propagation effects have become essential tools for interpreting observational data and testing source models [28]. As experimental precision continues to improve, particularly through observatories such as the Pierre Auger Observatory, a more coherent picture of UHECR propagation is gradually emerging, bringing us closer to unveiling their astrophysical origins.

Figure 4. Comparison of simulated UHECR energy spectra for four source composition models. The gray curve represents the total predicted spectrum, colored curves show the contributions from different nuclear mass groups, and blue points denote Pierre Auger Observatory data. The figure highlights the influence of source composition on the observed UHECR spectrum under identical propagation conditions [27].

Observing ultra-high-energy cosmic rays (UHECRs) is an exercise in reading cosmic footprints rather than catching the particles themselves. Because the flux of UHECRs is extremely low, direct detection above 10¹⁸ eV is impractical. Instead, experiments rely on the observation of extensive air showers (EAS) produced when primary cosmic rays interact with nuclei in Earth’s atmosphere. These cascades of secondary particles spread over vast areas and carry imprints of the primary particle’s energy, mass, and arrival direction, allowing indirect reconstruction through sophisticated detection techniques [29][30]. One of the primary methods employed is the use of ground-based surface detector arrays, which sample secondary particles at ground level. These detectors, typically spaced over large regions (hundreds to thousands of square kilometers), measure the lateral distribution and timing of particles in the air shower. For example, the Pierre Auger Observatory utilizes an array of water-Cherenkov detectors, while the Telescope Array Project employs scintillation counters. By analyzing the particle densities and arrival times across the array, the direction and energy of the primary UHECR can be reconstructed with high accuracy [31][32].

Complementing surface arrays are fluorescence detectors, which observe the faint ultraviolet light emitted when charged particles in the air shower excite atmospheric nitrogen molecules. This technique provides a nearly calorimetric measurement of the shower energy by tracking its longitudinal development through the atmosphere. Fluorescence telescopes operate primarily on clear, moonless nights, limiting their duty cycle but offering crucial insights into the depth of shower maximum (X_max), a key observable for determining the mass composition of UHECRs [33]. Hybrid detection, combining surface and fluorescence techniques, as implemented at the Pierre Auger Observatory, significantly improves reconstruction accuracy and reduces systematic uncertainties. In addition to these established methods, radio detection techniques have gained increasing attention in recent years. Air showers emit coherent radio signals due to geomagnetic effects and charge-excess processes, which can be detected by ground-based antenna arrays. Radio detection offers a highdutycycle alternative to fluorescence measurements and provides complementary information on shower properties, particularly energy and geometry [34]. Experiments such as LOFAR and AERA (Auger Engineering Radio Array) have demonstrated the viability of this technique for precision studies of UHECRs.

Another emerging approach involves the detection of Cherenkov radiation, both in the atmosphere and in dense media such as ice or water. While atmospheric Cherenkov techniques are more commonly used for gamma-ray astronomy, they also contribute to cosmic ray studies at lower energies. In dense media, large-scale detectors can observe Cherenkov light produced by secondary particles, providing an additional channel for highenergy particle detection. For instance, the IceCube Neutrino Observatory primarily detects neutrinos but also contributes indirectly to UHECR studies through the observation of secondary particles generated in cosmic ray interactions [35]. Looking ahead, next-generation and space-based observatories aim to extend the reach of UHECR observations. Proposed missions such as POEMMA (Probe of Extreme Multi-Messenger Astrophysics) plan to detect fluorescence and Cherenkov signals from space, enabling the monitoring of vast areas of Earth’s atmosphere and dramatically increasing the exposure to the rarest, highest-energy events [36]. These future instruments, combined with advances in data analysis and simulation, are expected to play a crucial role in resolving the origin and nature of UHECRs.

Despite significant progress in both observational and theoretical studies, the origin and nature of ultra-high-energy cosmic rays (UHECRs) remain unresolved. Several key challenges continue to limit a comprehensive understanding of these particles, arising from uncertainties in measurements, modeling, and interpretation. One of the primary challenges is the uncertainty in mass composition at the highest energies. The composition of UHECRs is inferred indirectly through extensive air shower observables such as the depth of shower maximum (X_max) and its fluctuations. However, these interpretations rely heavily on hadronic interaction models extrapolated beyond the energy range tested in terrestrial accelerators. Measurements from the Pierre Auger Observatory suggest a transition toward heavier nuclei at higher energies, whereas results from the Telescope Array Project are consistent with a lighter composition within uncertainties [2][10]. This discrepancy highlights the need for improved modeling of high-energy particle interactions.

Another major difficulty is the identification of astrophysical sources. Charged cosmic rays are deflected by galactic and extragalactic magnetic fields during propagation, which obscures the correlation between their arrival directions and their sources. Although large-scale anisotropies have been observed, including a dipole pattern reported by the Pierre Auger Observatory, the exact sources responsible for UHECRs have not been conclusively identified [3][13]. A further limitation arises from the low flux of UHECRs at the highest energies. The number of detected events above 10²⁰ eV is extremely small, even for large observatories. This restricts the statistical significance of anisotropy studies and limits the ability to distinguish between competing theoretical models. Increasing the exposure and sensitivity of experiments is therefore essential for improving the reliability of observational results [2].

The uncertainty in extragalactic magnetic fields (EGMFs) also presents a significant challenge. The strength, structure, and distribution of these fields are not well constrained, yet they play a crucial role in determining the propagation paths of UHECRs. Variations in magnetic field models can lead to different interpretations of arrival direction data and source correlations [37]. In addition, systematic uncertainties in energy calibration across different experiments complicate comparisons of observational results. Slight differences in the measured energy spectrum between the Pierre Auger Observatory and the Telescope Array Project affect the interpretation of key spectral features such as the ankle and the high-energy suppression [4][10]. Finally, there exists a degeneracy between source properties, composition, and propagation effects. For example, the observed suppression at the highest energies may result either from the maximum energy achievable at the source or from propagation effects such as the Greisen-Zatsepin-Kuzmin cutoff. Similarly, different combinations of source distributions and magnetic field configurations can produce similar observational signatures, making it difficult to uniquely constrain theoretical models [3]. The study of UHECRs is currently limited by uncertainties in composition, source identification, magnetic field modeling, and experimental calibration. Addressing these challenges will require advances in detector technology, improved theoretical models, and continued integration of multi-messenger observations.

In spite of many years of observational and theoretical advances, the origin of ultra-high energy cosmic rays is one of the most enduring mysteries of high energy astrophysics. One of the key difficulties is that of particle deflection due to Galactic and extragalactic magnetic fields, which makes it difficult to identify their sources due to distortion of their arrival directions. Though a large scale dipole anisotropy has been detected for energies >~8 EeV, its interpretation is not straightforward due to the uncertainties regarding magnetic field structure and the nature of primaries [38][39]. As a result, it is difficult to identify strong correlations between the sources of UHECRs and their possible counterparts like AGNs, GRBs, or starburst galaxies. Another major difficulty is related to the composition of UHECRs. Recent measurements suggest a trend toward heavier nuclei at the highest energies, but discrepancies between major experiments such as the Pierre Auger Observatory and the Telescope Array persist [39][40].

Given that acceleration processes and propagation processes are highly dependent on the charge and mass of the particles, this ambiguity will affect the source models as well. In addition to that, the energy spectrum suppression of cosmic rays above ~4 × 10¹⁹ eV can be the result of energy loss due to cosmic microwave background interaction through the Greisen-Zatsepin-Kuzmin effect or due to the limitations of the astrophysical sources [40]. Multi-messenger astrophysics is one promising path that could take us forward. The detection of high-energy neutrinos and gamma rays gives us complementary information regarding high-energy astrophysical phenomena and UHECR sources. The fact that neutrinos propagate almost unaltered and unaffected and that high-energy gamma rays get attenuated due to their interaction with background radiation fields makes multi-messenger astrophysics a possible way to constrain source models and the acceleration mechanisms [38]. But the current sensitivities and statistics of events still fall short, and our current neutrino measurements limit the sources and propagation theories of UHECRs, but have not yet pinpointed their sources.

Future experimental studies have been forecast to be critical in solving these problems. The developments like Auger Prime, which intend to improve the mass composition measurements using advanced detectors, and other future experiments like GRAND and POEMMA will extend exposure and energy range. These developments will allow high statistics data sets, enhanced anisotropy searches, and improved discriminating between the source models [41]. In addition to this, theoretical work is also moving towards developing realistic models of cosmic ray transport in structured magnetic fields and the modeling of possible sources, such as relativistic jets, magnetars, and black holes [42]. Particle transport simulations like CRPropa can model particle interactions with cosmic magnetic fields and radiation background, providing a more accurate comparison with the observations. As observational precision improves and multi-messenger data become increasingly integrated, the coming decade is expected to significantly narrow down the list of viable UHECR sources, potentially leading to the first definitive identification of their astrophysical origins [28]. Improved modeling of Galactic and extragalactic magnetic fields will further help reduce uncertainties in tracing cosmic-ray trajectories back to their sources.

Moreover, space-based techniques can also provide a larger observational exposure compared to traditional ground-based approaches. For instance, POEMMA will utilize space-borne techniques to detect extensive air showers through the observation of fluorescence and Cherenkov radiation in large regions of the Earth’s atmosphere. This will help in increasing the number of observed events especially at high energy levels [36].

Even with such advances, however, some issues still need clarification. How the contributions of various sources are distributed, how the changeover from Galactic to extragalactic origin of cosmic rays occurs, and what is the composition at ultra-high energies are only some of the questions which have yet to be answered. Besides, the influence of properties of sources and the effects of propagation on interpreting observational data makes the problem even more complicated. However, the combination of achievements in these four areas is likely to considerably reduce the number of potential sources of ultra-high energy cosmic rays and reveal their true origin.

Ultra-high-energy cosmic rays (UHECRs) represent one of the most extreme phenomena in the universe, carrying energies that challenge current understanding of particle acceleration and astrophysical processes. Over the past decades, significant progress has been achieved through observations by major facilities such as the Pierre Auger Observatory and the Telescope Array Project, which have provided detailed measurements of the energy spectrum, composition, and anisotropy of UHECRs. These observations strongly support an extragalactic origin for the highest-energy particles and reveal key spectral features such as the ankle and the high-energy suppression. A range of astrophysical sources, including active galactic nuclei, gamma-ray bursts, starburst galaxies, and compact objects such as magnetars, have been proposed as potential accelerators of UHECRs. The feasibility of these sources is generally constrained by the Hillas criterion, which links the maximum achievable energy to the size and magnetic field strength of the acceleration region. While several candidate sources satisfy these requirements, no single class has yet been conclusively identified as the dominant contributor.

The propagation of UHECRs through intergalactic space introduces additional complexity, as interactions with background radiation fields lead to energy losses, most notably through the Greisen-Zatsepin-Kuzmin cutoff, and magnetic deflections obscure the connection between observed arrival directions and source locations. These effects, combined with uncertainties in mass composition and magnetic field structure, continue to complicate the interpretation of observational data. Recent developments in multi-messenger astronomy, including the detection of high-energy neutrinos by the IceCube Neutrino Observatory, have opened new pathways for investigating the origin of UHECRs. By combining information from cosmic rays, neutrinos, and gamma rays, it is becoming possible to place stronger constraints on source models and acceleration mechanisms. At the same time, ongoing and planned upgrades to existing observatories, along with future space-based missions, are expected to significantly enhance observational capabilities.

Despite these advances, several fundamental questions remain unresolved, including the precise composition of UHECRs at the highest energies, the identification of their dominant sources, and the mechanisms responsible for their acceleration. Addressing these challenges will require continued improvements in experimental techniques, theoretical modeling, and the integration of multi-messenger data. In conclusion, while the origin of ultra-high-energy cosmic rays is not yet fully understood, the combination of increasingly precise observations and advanced theoretical frameworks is steadily narrowing the range of possibilities. Continued efforts in this field are expected to provide deeper insights into the most energetic processes in the universe and may ultimately lead to a definitive understanding of the sources of UHECRs.

Anaya Vachhani conceptualized the study, performed the literature search and analysis, and drafted the manuscript. Sananjay Biswas contributed to the literature survey, scientific interpretation, and critical revision of the manuscript. Anaya Vachhani and Sananjay Biswas discussed the findings and contributed to the final review and editing of the manuscript. Both authors read and approved the final manuscript.