Probing Gravitation, Dark Energy, and Acceleration

TL;DR

The paper tackles the origin of cosmic acceleration by contrasting dark energy with modified gravity, unifying the expansion history and geometry under a common framework. It develops a general parametrization of deviations from the Friedmann equation via $\delta H^2$, linking it to an effective $w_{\rm DE,eff}(z)$, and introduces a geometric viewpoint through the Ricci scalar with a central descriptor ${\cal R}=R/(12H^2)$. Through explicit models (braneworld and vacuum metamorphosis) and phenomenological cases, it shows that distance-based probes and growth of structure can be highly degenerate between gravity and dark-energy explanations, though higher-order probes like ISW and CMB lensing may help distinguish them. The work argues for a robust two-parameter description of dark energy with $w_0$ and $w_a$, while highlighting the pivotal role of the Ricci-geometry perspective in interpreting acceleration and guiding future observational strategies to identify the underlying physics.

Abstract

The acceleration of the expansion of the universe arises from unknown physical processes involving either new fields in high energy physics or modifications of gravitation theory. It is crucial for our understanding to characterize the properties of the dark energy or gravity through cosmological observations and compare and distinguish between them. In fact, close consistencies exist between a dark energy equation of state function w(z) and changes to the framework of the Friedmann cosmological equations as well as direct spacetime geometry quantities involving the acceleration, such as ``geometric dark energy'' from the Ricci scalar. We investigate these interrelationships, including for the case of superacceleration or phantom energy where the fate of the universe may be more gentle than the Big Rip.

Figures (5)

• Figure 1: The growth factor behavior $\delta/a$ for two modified gravitation models is compared with that of dark energy models. A clear distinction can be seen relative to the cosmological constant, $\Lambda$, model, but simple time varying dark energy models (short dashed, red curves) can be found that reproduce the modified gravity.
• Figure 2: The gravitational potential $\Phi(z)$ for the same models as Fig. \ref{['fig.grobwvm']} is plotted vs. redshift, showing the decay of the potential as the expansion accelerates. Dashed, red curves are for the mimicking $(w_0,w_a)$ models. The dotted outliers to the cosmological constant curve show the deviation expected by a misestimation of the matter density $\Omega_m$ by 0.02. The discrimination of modified gravity from a cosmological constant is clear, but from the fit dark energy models is problematic.
• Figure 3: The effective equations of state corresponding to the modified Friedmann equations (\ref{['eq.case1']}-\ref{['eq.case3']}) are plotted vs. redshift. The parameter space allowed under CMB constraints for Cases 1 and 2 lie between the respective curves shown and the $w=-1$ line, i.e. they can mimic a cosmological constant arbitrarily closely. Case 3 curves (labeled by value of $B$) can fit the CMB distance of the $\Lambda$ model with much more strongly varying equations of state, lying between the left and right solid curves, with a perfect fit given by the middle solid curve.
• Figure 4: As Fig. \ref{['fig.grobwvm']} but for Case 3 modified gravity. A fairly clear distinction in growth behavior exists relative to the cosmological constant model, but not with respect to each corresponding, simple, time varying dark energy (dashed, red curves). These were chosen to match the magnitude-redshift relation, so neither expansion history nor growth history here distinguishes between a gravitational and dark energy explanation for the acceleration of the universe.
• Figure 5: The gravitational potential behavior as in Fig. \ref{['fig.potlbwvm']}, but for the Case 3 modified models (black solid curves) and dark energy models (red dashed curves, blue dotted curve for $w=-1$) in Fig. \ref{['fig.grodhw']}.