Cosmic acceleration in a dust only universe via energy-momentum powered gravity

We propose a modified theory of gravitation constructed by the addition of the term $f(T_{\mu \nu }{T}^{\mu \nu })$ to the Einstein-Hilbert action, and elaborate a particular case $f(T_{\mu \nu }{T}^{\mu \nu })=\alpha (T_{\mu \nu }{T}^{\mu \nu }{)}^{\eta }$, where $\alpha$ and $\eta$ are real constants, dubbed energy-momentum powered gravity (EMPG). We search for viable cosmologies arising from EMPG, especially in the context of the late-time accelerated expansion of the Universe. We investigate the ranges of the EMPG parameters $(\alpha ,\eta )$ on theoretical as well as observational grounds leading to the late-time acceleration of the Universe with pressureless matter only, while keeping the successes of standard general relativity at early times. We find that $\eta =0$ corresponds to the $\mathrm{\Lambda }\mathrm{CDM}$ model, whereas $\eta \ne 0$ leads to a $w\mathrm{CDM}$-type model. However, the underlying physics of the EMPG model is entirely different in the sense that the energy in the EMPG Universe is sourced by pressureless matter only. Moreover, the energy of the pressureless matter is not conserved, namely, in general it does not dilute as $\rho \propto a^{-3}$ with the expansion of the Universe. Finally, we constrain the parameters of an EMPG-based cosmology with a recent compilation of 28 Hubble parameter measurements, and find that this model describes an evolution of the Universe similar to that in the $\mathrm{\Lambda }\mathrm{CDM}$ model. We briefly discuss that EMPG can be unified with Starobinsky gravity to describe the complete history of the Universe including the inflationary era.

Figure 1

$q$ versus $\frac{{\rho }_{\mathrm{m}}}{{\rho }_{\mathrm{m},0}}$ curve of the $w\mathrm{CDM}$ and EMPG models. The figure is plotted by using ${\mathrm{\Omega }}_{\mathrm{m},0}=0.305\pm 0.010$ and $w_{\mathrm{DE}}=-0.97\pm 0.05$, corresponding to ${\alpha }^{\prime }=2.28\pm 0.11$ and $\eta =0.015\pm 0.025$ according to the transformations between the two models, from the constraints for the $w\mathrm{CDM}$ model from $\text{Planck}+\mathrm{BAO}+\mathrm{SN}$ data presented in Ref. [9].

Figure 2

$1\sigma$ and $2\sigma$ confidence contours of the EMPG model parameters. Marginalized probability distributions of the individual parameters are also displayed.

Figure 3

$H(z)/(1+z)$ curves of the EMPG and $\mathrm{\Lambda }\mathrm{CDM}$ models are plotted with the mean values and $1\sigma$ error regions of the model parameters. The 28 $H(z)$ data points of Table 1 are also displayed.

Figure 4

The mean value deceleration parameter curves with $1\sigma$ error regions of the EMPG and $\mathrm{\Lambda }\mathrm{CDM}$ models are plotted in the redshift range (0, 1100) (log scale on the $z$ axis) with the mean values of the model parameters.

Figure 5

The mean value jerk parameter curves with $1\sigma$ error regions of the EMPG and $\mathrm{\Lambda }\mathrm{CDM}$ models are plotted in the redshift range (0, 1100) (log scale on the $z$ axis) with the mean values of the model parameters.

Figure 6

Constraints in the $\eta \text{−}\alpha$ plane with $1\sigma$ and $2\sigma$ confidence level contours from $H(z)$ data in the EMPG model where the samples are coloured by the parameter ${\alpha }^{\prime }$.

Figure 7

The relative error $\delta {\rho }_{\mathrm{m}}/{\rho }_{\mathrm{m}}$ versus ${\rho }_{\mathrm{m}}/{\rho }_{\mathrm{m},0}$ from ${\rho }_{\mathrm{m}}/{\rho }_{\mathrm{m},0}=1$ ($z=0$) to ${\rho }_{\mathrm{m}}/{\rho }_{\mathrm{m},0}={10}^9$ $(z\sim 1100)$ for the mean values ${\alpha }^{\prime }=2.8$, $\eta =-0.003$ given in Table 2.