Cosmology is beset with many challenging questions and lacunae, which bring into question the standard model of cosmology (SMC) [1] [2] itself. Prominent amongst these challenges are the Hubble tension, dark matter and dark energy, inflation, accelerated expansion, and high red shift galaxies [3] . In addition, there are the horizon and flatness problems [4] , baryon asymmetry [5] , singularity conditions, etc. Accelerated expansion of the universe [6] [7] , often attributed—somewhat speculatively—to a repulsive dark energy component, further adds to the mounting number of unexplained phenomena. Recent observations of large high redshift galaxies by JWST have the scientific community wondering about the Big Bang and the evolutionary timeline of the universe.

In this paper, we adopt an observer-centric approach to study the evolutionary time line and age of the universe (AoU). This approach, different from the “co-moving galaxy” approach widely used, enables us to view space, time, age, and evolution of the universe in a new light and from the viewpoint of a “present day” observer on earth. This approach offers a reconciliation of the observational and theoretical lacunae with respect to the age and allowable evolutionary time for the observed high redshift galaxies.

JWST (NASA, 2025) [8] , since its launch in 2021, while providing a wealth of cosmological data and revealing many new objects and phenomena in deep space, to some extent, seems to have further widened the gaps in our understanding of how the universe works, evolves or exists. A large number of high red shift galaxies at z > 10 observed [9] - [13] seem to defy the prevalent and widely accepted age and timeline of the universe. The latest JWST observed galaxy, MoM-z14, which is nearly 500 million light-years across (Naidu et al., 2025) [13] with the highest confirmed redshift of 14.44, corresponding to an assessed epoch just 280 million years after the Big Bang, is surprisingly luminous for its epoch and challenges conventional models that predict fainter and smaller galaxies in that epoch. It is felt that such large galaxies will take much longer to evolve (Henriques et al., 2014) [14] . According to the largely accepted cosmic timeline ( Figure 1 and Figure 2 ), the first stars appeared at around 200 million years after the Big Bang and the first galaxies after 400 million years [15] . High red shift galaxies such as MoM-z14 raise fundamental question about galaxy formation in a period of few hundred million years after the Big Bang. Either the largely accepted timeline of the universe ( Figure 1 and Figure 2 ) is somewhat misleading, or we are missing something in the physics of the universe and the Star Formation Rates (SFR) [14] .

On the other hand, Hubble tension [15] - [17] , which is the discrepancy in the assessed value of the Hubble constant by different methodologies, remains a bone of contention. Two of the most important studies in cosmology are the Planck Collaboration 2018 [16] using the ΛCDM with cosmic microwave background (CMB) [18] and the Cepheid Variable study [19] . CMB is believed to be the earliest relic of the universe, detected by us, from an estimated time of almost 380,000 years after the Big Bang. The two studies have come up with a significant 5σ tension in Hubble constant values.

Measurements arrived at through 42 local Type Ia supernovae (SNe Ia) calibrated by Cepheid variables [20] yielded H₀ = 73.0 ± 1.0 km/s/Mpc, and the Planck observations of the CMB [16] [21] predicted H₀ = 67.4 ± 0.5 km/s/Mpc [22] . Riess et al. (2023) [23] , through JWST observations, revalidate the accuracy

of H₀ derived earlier by them at 74.03 ± 1.42 km/s/Mpc [24] . Both studies estimate age of the universe at around 13.79 Gyrs and both appear to be the most comprehensive studies with little room for bridging the gap or tension, unless something very different is assumed at a fundamental level.

A fundamental underlying aspect of the cosmology, early universe dynamics, and the age of the universe (AoU) has to do with our understanding of the flow or passage of time as we assess age of stars and galaxies at 10+ Gyrs or examine near singularity conditions. If the passage of time is not properly understood and not treated well, there can be implications on SFRs or the Galaxy Formation Rates (GFR).

In this paper, we delve deeper into concepts of time and distance and examine if, in the context of General Theory of Relativity (GTR), these parameters have been treated correctly and appropriately from the perspective of an observer on earth.

An important question in modern cosmology and the standard model (SMC) is the age of the universe (AoU). By most of the different methods, AoU has been assessed and reported at around 13.79 Gyr, as can be seen in Table 1 . A fundamental question that arises with respect to the AoU is that given the relative nature of “time” in GTR, is it being treated in a manner that gives us the correct perspective on the AoU from the viewpoint of an observer on earth in the present time and if AoU, pegged at 13.79 Gyr, is the same “time” or the “proper time” that we perceive or is it something different?

For a ray of light emitted at the dawn of the universe, reaching us through many epochs under accelerated expansion of the universe, varying matter density, time dilation, length contraction, and many other known and unknown effects such as gravitational lensing, quantum effects and entanglement, influences of dark matter, and dark energy—are we able to correctly assess the passage of time and the distances involved for this ray of light? In our opinion, there remains lack of conceptual clarity on “AoU” and treatment of “time” and “distance”, which we have dealt with in subsequent sections of this paper.

AoU time assessed at 13.79 Gyrs is not necessarily in the same unit of time that an observer assesses on earth now. The unit of measurement of AoU, also termed as “The Cosmic Time”, which in a homogeneous and isotropic universe, described by the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, is the “proper time” experienced by a comoving observer who is at rest relative to the average motion of the cosmos. For such an observer, “cosmic time” and “proper time” coincide. In reality, however, no such observer exists; it remains only a theoretical construct.

When we look back from the current time, which is the “proper time” for an observer on earth, it is not necessarily equivalent to the “cosmic time.” There is also no mathematical proof establishing equivalence of “cosmic time” and the

“proper time.” It is important to keep in mind that in order to perceive “time” and “distances”, in general in GTR, an observer is must and such an observer has to be in the present. The concept of the “existence of the observer” and what constitutes an observation is essential and fundamental aspect of physics [25] and theoretical constructs that by-pass observation and the observer can at best be termed as “speculative.” Therefore, because the AoU assessed at 13.79 Gyrs is based on comoving framework, it should be seen as a speculative number and should be critically examined under the GTR framework.

We, as the present observers on earth, can look at time lapse in AoU in three ways—AoU (type 1)—The “cosmic time” assessed at 13.79 Gyr, which is the prevailing concept and largely accepted; AoU (type 2)—In the units and measures of the time elapsed i.e., in the “number” of solar years or solar Gyrs irrespective of the fact that these years in the past epochs would have been longer due to time elongation, and the Effective AoU (type 3)—In the units that are corrected to current proper time taking into account time elongation. We find that in literature, however, while referring or reporting AoU, no distinction is made amongst the different types and the AoU is assumed to be (type 1). In both type 1 AoU and type 2 AoU, each unit of time considered is equal, be it at 1Gyr epoch or 12 Gyr epoch in the timeline. It is as if time is recorded on a counter and each value of the counter is same. With homogeneity and isotropy assumptions of the universe, type 1 and type 2 should be nearly equal and this is how type 1 AoU is justified.

Type 1 AoU is calculated using the scale factor in FLRW equations as described here.

Scale factor for comoving objects and observers is a part of SMC, also known as the Lambda-Cold Dark Matter (ΛCDM) model, which describes the evolution of the universe from the moment of Big Bang to its present state.

In SMC, Einstein’s General Theory of Relativity (GTR) [26] [27] forms the main underlying basis of the four-dimensional ΛCDM model given by:

$G^{\mu v}+\Lambda g^{\mu v}=\frac{8\pi G}{c^4}{T}^{\mu v}$ (1)

where:

$G^{\mu v}$ is the Einstein Tensor, $T^{\mu v}$ is the Energy Momentum Stress Tensor, $g^{\mu v}$ is the metric tensor, and Λ is the cosmological constant.

The metric that satisfies both the cosmological principles of homogeneity and isotropy with time dependent scale factor a(t) is given by the Robertson and Walker metric, as:

$\text{d}{s}^2=-c^2\text{d}{t}^2+a{\left(t\right)}^2\left[\frac{\text{d}{r}^2}{1-k{r}^2}+r^2\text{d}{\omega }^2\right]$ (2)

where,

$\text{d}{\omega }^2=\text{d}{\theta }^2+{\sin }^2\theta \text{d}{\varphi }^2$ (3)

r, $\theta$, and $\varphi$, are the spherical coordinates for the metric. The parameter k = +1, 0, −1 denotes closed, flat, and open geometries, respectively.

With Equations (1) and (2), the Friedmann equations are obtained:

${\left(\frac{\stackrel{\dot{}}{a}}{a}\right)}^2=\left(\frac{8\pi G}{3}\right)\rho -\frac{k{c}^2}{a^2}+\frac{\Lambda c^2}{3}$ (4)

and,

$\frac{\ddot{a}}{a}=-\frac{4\pi G}{3}\left(\rho +\frac{3p}{c^2}\right)+\frac{\Lambda c^2}{3}$ (5)

Equation (4) can be rewritten in terms of the Hubble’s parameter as:

$H^2=\frac{8\pi G}{3}\left(\rho +{\rho }_{\Lambda }\right)-\frac{k{c}^2}{a^2}$ (6)

where, ${\rho }_{\Lambda }=\frac{\Lambda c^2}{8\pi G}$.

In terms of dimensionless densities, the Friedmann equations can be written as:

$H^2=H_0^2\left(\frac{{\Omega }_{m,0}}{a^3}+\frac{{\Omega }_{r,0}}{a^4}+{\Omega }_{\Lambda ,0}+\frac{{\Omega }_{K,0}}{a^2}\right)$ (7)

At present a = 1, therefore:

${\Omega }_{k,0}=1-{\Omega }_{m,0}-{\Omega }_{\Lambda ,0}-{\Omega }_{r,0}$ (8)

where,

$H_0$ is the Hubble’s constant at present time and Ω are the dimensionless densities corresponding to matter (baryonic + dark), radiation, and darkenergy as given below:

${\Omega }_m\left(a\right)=\frac{{\rho }_m\left(a\right)}{{\rho }_{crit}\left(a\right)}$ (9)

${\Omega }_r\left(a\right)=\frac{{\rho }_r\left(a\right)}{{\rho }_{crit}\left(a\right)}$ (10)

${\Omega }_{\Lambda }\left(a\right)=\frac{{\rho }_{\Lambda }\left(a\right)}{{\rho }_{crit}\left(a\right)}$ (11)

${\Omega }_{m,0}$, ${\Omega }_{r,0}$, and ${\Omega }_{\Lambda ,0}$ are the present values and

${\rho }_m\propto a^{-3}$ (12)

${\rho }_r\propto a^{-4}$ (13)

The critical density of the universe, for it to be flat at any time t is given by:

${\rho }_{crit}=\frac{3H^2}{8\pi G}$ (14)

If the actual density $\rho$ is greater than ${\rho }_{crit}$, the universe is closed and will eventually stop expanding and re-collapse.

If $\rho$ is equal to ${\rho }_{crit}$, the universe is flat and will continue to expand forever at a decreasing rate.

If $\rho$ is less than ${\rho }_{crit}$, the universe is open and will expand forever at an increasing rate.

In a flat universe, The matter density ${\rho }_m$ scales with the expansion of the universe as:

${\rho }_m={\rho }_{m,0}{\left(1+z\right)}^3$ (15)

Assuming dark energy density as constant we have from Equation (7)

$H^2=H_0^2\left({\Omega }_{m,0}{\left(1+z\right)}^3+{\Omega }_{\Lambda }\right)$ (16)

The Hubble parameter can also be expressed in terms of the scale factor “a”:

$H_{\left(a\right)}=\frac{\stackrel{\dot{}}{a}}{a}$ (17)

Now,

$1+z=\frac{a_0}{a}$ (18)

where a₀ is the scale factor at present, set at a₀ = 1. Therefore:

$z=\frac{1}{a}-1$ (19)

On substituting this into the Friedmann equation, we get:

$H^2=H_0^2\left({\Omega }_m{\left(\frac{1}{a}\right)}^3+{\Omega }_{\Lambda }\right)$ (20)

H is then given by:

$H=H_0\sqrt{\frac{{\Omega }_m}{a^3}+{\Omega }_{\Lambda }}$ (21)

or

$H=H_0\sqrt{\left({\Omega }_m{\left(1+z\right)}^3+{\Omega }_{\Lambda }\right)}$ (22)

AoU, “t₀”, which is the age of the universe at present, can be calculated with the integral:

$t_0={\displaystyle \underset{0}{\overset{1}{\int }}\frac{\text{d}a}{aH\left(a\right)}}$ (23)

Using Equation (21) we have

$t_0={\displaystyle \underset{0}{\overset{1}{\int }}\frac{\text{d}a}{a{H}_0\sqrt{\frac{{\Omega }_m}{a^3}+{\Omega }_{\Lambda }}}}$ (24)

On substituting “a” from Equation (17) we have:

$\text{d}a=-\frac{\text{d}z}{{\left(1+z\right)}^2}$ (25)

Thus AoU in terms of z is given by:

$t_0=\frac{1}{H_0}{\displaystyle \underset{0}{\overset{\infty }{\int }}\frac{\text{d}z}{\left(1+z\right)\sqrt{{\Omega }_m{\left(1+z\right)}^3+{\Omega }_{\Lambda }}}}$ (26)

Time elapsed from any epoch at z will be given by:

$T\left(z\right)={\displaystyle \underset{z}{\overset{\infty }{\int }}\frac{1}{\left(1+z^{\prime }\right)H\left(z^{\prime }\right)}\text{d}{z}^{\prime }}$ (27)

where z' is the integration variable.

The standard cosmological framework expresses the age of the universe at a given redshift z through the integral of the inverse Hubble parameter, weighted by (1 + z')⁻¹, as shown in Equation (27). While this provides a proper time for a co-moving observer since the Big Bang, it does not account for the relativistic time dilation experienced by observers at different epochs. In particular, during earlier cosmic times, the universe expanded significantly faster, and physical processes (such as star formation, cooling, and gravitational collapse) occurred under substantially dilated time intervals when viewed from the present epoch.

Identifying 10 spectroscopically confirmed and robustly identified high‑z galaxies (z ≈ 10 - 20), we mapped their redshifts to EAoU times, spanning approximately 9 to 14.5 Gyr (See Table 3 and Table 4 ). For comparison, standard cosmic ages at these redshifts are merely 0.3 - 0.5 Gyr post-Big Bang. The EAoU framework thus provides significantly extended evolutionary clock time, supporting the assembly of ~10⁹ M_☉ stellar masses and vigorous SFRs (≈ 20 - 100 M_☉/yr). Notably, HD1 and HD2 (z ≈ 13) emerge at EAoU ≈ −11.5 Gyr, a window consistent with sustained star formation rates needed to build ~10⁹ M_☉ in stellar mass.

These 10 representative high-redshift galaxies, spanning z ≈ 9 - 16, exhibit star formation rates (SFRs) from ~20 M_☉/yr up to ~120 M_☉/yr and stellar masses of ~10⁹ M_☉—remarkably high given their young cosmic ages under standard cosmology (≈300 - 500 Myr post-Big Bang). Interpreting their timelines within the EAoU framework (with EAoU₀ ≈ 45 Gyr) yields effective ages of ~36 - 44 Gyr, significantly extending their effective growth time. This extended timescale alleviates the tension between observed high SFRs/stellar masses and limited cosmic time in ΛCDM. For instance, GNz11 (z = 10.60, SFR ≈24 M_☉/yr, M ≈ 10⁹ M_☉) has an EAoU-derived age of ~38 Gyr, as opposed to only ~430 Myr in conventional terms. Similarly, HD1 and GSz140—at z ≈ 13 - 14 and boasting SFRs of ~100 - 120 M_☉/yr—attain EAoU ages of ~42 - 43 Gyr, offering a plausible evolutionary window for their observed properties. These findings directly support our thesis that an EAoU ~45 Gyr can naturally accommodate the early assembly of massive, star-forming galaxies without invoking exotic astrophysics.

We have categorized and redefined the Age of the Universe (AoU) under three distinct types:

Using Friedmann-Lemaître-Robertson-Walker (FLRW) equations, we estimate the EAoU to lie in the range of ~40 - 45 Gyr, depending on the chosen cosmological scenario. These estimates correspond to epochs when the scale factor was only 0.005 - 0.0062 (about 0.5% - 0.62% of its present value), implying that the universe’s linear dimensions were smaller by a factor of roughly 160 - 200.

The revised understanding of AoU directly impacts our interpretation of cosmic evolution, particularly the rates of star and galaxy formation (SFR/GFR). While the EAoU framework does not challenge the foundations of the ΛCDM model, it augments it with a relativistically consistent temporal metric, offering an alternative perspective more aligned with observational anomalies such as high-redshift, evolved galaxies seen in JWST and Hubble data.

This paper does not dispute any existing cosmological theory but introduces EAoU as a supplementary parameter, potentially resolving the paradox of early massive galaxy formation without invoking exotic physics.

Viewed through a thermodynamic lens, the EAoU framework links cosmic time to the irreversible growth of entropy and the scaling of temperature with expansion. While speculative, this perspective suggests a deeper connection between spacetime evolution and the second law of thermodynamics, pointing to an entropic foundation for cosmic chronology.

That said, a certain level of uncertainty remains—especially regarding the rate of natural processes under extreme time dilation. For example, it is unclear whether 1 Gyr at a Time Dilation Factor (TDF) of 50 is functionally equivalent to 1 Gyr at TDF = 1 in terms of entropy progression, star formation, or structure growth. This has broader implications not only for the early universe but also for environments near black holes and other regions of intense gravitational curvature.

No empirical studies have yet addressed how process rates vary under extreme relativistic conditions, and such experimentation is inherently difficult. Nonetheless, this is an open domain of inquiry deserving serious theoretical and conceptual attention.

A related preprint elaborating the observational consequences of EAoU is available at Hossain, J. (2025) [58] . Effective Age of the Universe: Application of Relativistic Time Dilation. ResearchGate.