Modified-Source Gravity and Cosmological Structure Formation

TL;DR

This work proposes Modified-Source Gravity (MSG), a class of infrared modifications to general relativity that eliminates the propagating scalar degree of freedom by encoding gravity's modification in a non-dynamical scalar ψ with an arbitrary potential U(ψ). The authors derive the modified Friedmann equation and show how ψ, determined algebraically by the matter content via dU/dψ − 4U = −T, leads to a density-dependent G_eff and a late-time acceleration without dark energy. Linear perturbation analysis reveals a scale-dependent, enhanced growth of structure and an amplified ISW signal, with the growth rate for a given mode eventually driven by the wavenumber k; they also present a concrete model that fits SNLS and CMB data, predicting observable distinctions from ΛCDM in the growth history and ISW correlations. The study emphasizes that distinguishing modified gravity from dynamical dark energy requires joint probes of expansion history and perturbation evolution, and it highlights the need for nonlinear simulations to fully capture MSG dynamics in the fully nonlinear regime.

Abstract

One way to account for the acceleration of the universe is to modify general relativity, rather than introducing dark energy. Typically, such modifications introduce new degrees of freedom. It is interesting to consider models with no new degrees of freedom, but with a modified dependence on the conventional energy-momentum tensor; the Palatini formulation of $f(R)$ theories is one example. Such theories offer an interesting testing ground for investigations of cosmological modified gravity. In this paper we study the evolution of structure in these ``modified-source gravity'' theories. In the linear regime, density perturbations exhibit scale dependent runaway growth at late times and, in particular, a mode of a given wavenumber goes nonlinear at a higher redshift than in the standard $Λ$CDM model. We discuss the implications of this behavior and why there are reasons to expect that the growth will be cut off in the nonlinear regime. Assuming that this holds in a full nonlinear analysis, we briefly describe how upcoming measurements may probe the differences between the modified theory and the standard $Λ$CDM model.

Figures (6)

• Figure 1: The potential $U$ (in units of $\rho_0$) and scalar field $\psi$ (in units of $M_{\rm P}$) as functions of the cosmological energy density $\rho$.
• Figure 2: The plot on the left shows the effective dark-energy density, in units of the matter density today, that observers would reconstruct. (That is, the dark-energy density that would lead to equivalent behavior for the scale factor if general relativity were correct.) The right plot shows the corresponding effective equation-of-state parameter as a function of redshift.
• Figure 3: The exponent of the growth of matter density perturbations, as defined in (\ref{['e:ge']}) for a selection of modes, solved for the model defined by (\ref{['model2']}) with the best fit parameters (\ref{['best-fit']})(near-horizon effects are ignored). The rate of growth is very strongly scale-dependent once the cosmology enters the epoch of acceleration, with the exponent departing sharply from $n=1$ and tending to $n \propto k$ at late times.
• Figure 4: The dimensionless matter power spectrum for MSG and $\Lambda$CDM. As expected, in MSG the growth-rate is proportional to $k$ and the power-spectrum increases exponentially with $k$ for modes within the horizon. Non-linear scales are reached at scales of $240$ Mpc ($k=0.004$ Mpc$^{-1}$), compared to $10$ Mpc$\equiv8h^{-1}$ Mpc for $\Lambda$CDM. The linear growth can only be trusted for $k<0.004$ Mpc$^{-1}$. For smaller scales, the theory should return to a GR-like behavior.
• Figure 5: The evolution of the quantity $\Phi-\Psi$---observable through the ISW effect---for modes close enough to the horizon to remain linear until today. In MSG, this combination of potentials grows during dark-energy domination, increasingly rapidly for higher $k$. This would lead to a significant increase in the ISW signal, at least for the lowest multipoles, which are sensitive only to the linear modes at largest scales. In LCDM this evolution is scale free.