The pseudo-complex Friedmann Lemaitre Robertson Walker model and the time dependence of the Hubble constant

TL;DR

The paper investigates a pseudo-complex extension of General Relativity (pcGR) that renders dark energy a geometric consequence and introduces a time-dependent Hubble parameter. By formulating a pcFLRW cosmology, the authors derive a Hubble function in which the dark-energy term scales as $(1+z)^{3(\beta-1)}$, with a single deformation parameter $\beta$ linked to the present-day Hubble evolution via $\beta = 1 + \tfrac{2}{3}\tfrac{\dot{H}_0}{H_0^2}$. Using DESI BAO data, they perform a full 13×13 covariance likelihood analysis of BAO observables $\left\{ \frac{D_V}{r_d}, \frac{D_M}{r_d}, \frac{D_H}{r_d} \right\}$ to constrain $\beta$, finding $\beta_{best} = 1.04261 \pm 0.0144$ and $w_\Lambda = -\beta \approx -1.0426$, consistent with a phantom-like effective fluid arising from geometry rather than exotic matter. The resulting $\dot{H}_0$ is nonzero, yielding a deceleration parameter $q \approx -0.936$ and a predicted redshift drift $\Delta v \approx -11.1$ cm s$^{-1}$ over 20 years at $z=4$, closely matching $\Lambda$CDM but differing in the underlying dynamics. The work shows that pcGR offers a testable, dynamically evolving alternative to $\Lambda$CDM, with redshift-drift measurements and future high-precision spectroscopy providing a concrete avenue to probe the geometric origin of dark energy.

Abstract

The pseudocomplex version of the FLRW model is presented within the framework of pseudocomplex General Relativity (pcGR). In this approach, dark energy arises as a geometric consequence of the pseudocomplex structure, leading to a time dependent Hubble parameter rather than a strictly constant H0. The relation between the tiderived and constrained using recent DESI BAO data. Fitting beta yields a best-fit value beta = 1.0426, corresponding to a deceleration parameter q = -0.9361 and a present day Hubble acceleration me derivative of the Hubble parameter and a single geometric parameter beta in the effective dark energy equation of state is derived and constrained using recent DESI BAO data. Fitting beta yields a best-fit value beta = 1.0426, corresponding to a deceleration parameter q = -0.9361 and a present day Hubble acceleration H0 sim 0.94 x10-17 (km/s2)/Mpc. Using the exact Sandage Loeb relation, the predicted redshift drift over 20 years for a source at z = 4 is Delta-v sim -11.1 cm/s, in close agreement with the Lambda CDM prediction. In pcGR, however, the non-vanishing H0 is a direct geometric prediction, providing a clear and testable target for future high-precision spectroscopic observations.

Figures (6)

• Figure 1: PCGR prediction for the Hubble distance $D_H(z)/r_d$ for different values of $\beta$. The broad dashed curve corresponds to the best-fit value $\beta = 1.0426$.
• Figure 2: PCGR prediction for the comoving angular diameter distance $D_M(z)/r_d$ for different values of $\beta$. The broad dashed curve indicates the best-fit value $\beta = 1.0426$.
• Figure 3: PCGR prediction for the volume-averaged distance $D_V(z)/r_d$ as a function of redshift for different values of the parameter $\beta$. The broad dashed curve corresponds to the best-fit value $\beta = 1.0426$.
• Figure 4: DESI BAO observables with $1\,\sigma$ error bars, constructed using the provided mean vector and covariance matrix, demonstrating the viability of the pcGR model given current data.
• Figure 5: The dependence of the $\chi^2$ function on the pcGR parameter $\beta$. The minimum at $\beta = 1.0426$ identifies the best-fit value from the DESI BAO likelihood analysis.