Unmodified Gravity

TL;DR

This paper investigates how non-gravitational interactions in the dark sector, specifically a decaying dark-energy component transferring energy to dark matter, alter the growth of cosmic structure. By deriving analytic growth-rate solutions, it shows the familiar growth relation $f(a) \approx \Omega_m(a)^{\gamma} - c$ acquires a constant offset $c$ proportional to the energy-transfer parameter $\epsilon$, with additional contributions from dilution and inertial drag. Including baryons modifies the effective decay through $\bar{\epsilon} = (\Omega_c/\Omega_m)\epsilon$, yielding $f(a) = \Omega_m(a)^{\gamma} - \frac{67}{55}\bar{\epsilon}$, while observational probes like redshift-space distortions and the ISW effect constrain $|\epsilon|$ to be small (e.g., $\epsilon \lesssim 0.1$). The work warns that neglecting dark-sector physics can bias growth-based tests of gravity, potentially mimicking modified gravity, and provides analytic tools to disentangle such effects.

Abstract

By relaxing the conventional assumption of a purely gravitational interaction between dark energy and dark matter, substantial alterations to the growth of cosmological structure can occur. In this work we focus on the homogeneous transfer of energy from a decaying form of dark energy. We present simple analytic solutions to the modified growth rates of matter fluctuations in these models, and demonstrate that neglecting physics within the dark sector may induce a significant bias in the inferred growth rate, potentially offering a false signature of modified gravity.

Figures (5)

• Figure 1: The fractional change in the evolution of linear perturbations in the presence of a decaying cosmological constant with $\epsilon=0.01$ (upper) and $\epsilon=0.04$ (lower), as defined in (\ref{['eq:epsi']}). The pair of dash-dotted lines highlight the slight suppression of growth induced by the diluting effect of transferring homogeneous energy into the dark matter frame. The dashed lines correspond to an energy transfer in the CMB rest frame, with the extra deceleration arising due to the introduction of stationary matter. These are well described by the solid lines, which illustrate the analytic solution given by (\ref{['eq:ana']}).
• Figure 2: The logarithmic growth rate of both cold dark matter (dashed), and the baryons (dotted), in the presence of a decaying cosmological constant with $\epsilon=0.04$. The solid line illustrates the approximate solution given by (\ref{['eq:ana2']}), which traces the total matter perturbation.
• Figure 3: The baryonic bias induced by $\epsilon=0.01$ and $\epsilon=0.04$.
• Figure 4: The solid contours provide an example of the bias which may be induced in the gravitational growth index $\gamma$ when making the false assumption that dark energy is stable. The true model, as indicated by the black dot, corresponds to $\epsilon=0.01$. The dashed contours demonstrate the modification to the growth index induced by the elastic interaction model outlined in simpscat.
• Figure 5: The decay rate of the gravitational potential as experienced in a flat $\Lambda \rm{CDM}$ Universe (solid), and with perturbed cosmologies $\epsilon=0.01$ (dashed) and $\Omega_k=-0.01$ (dotted).