Separating Dark Physics from Physical Darkness: Minimalist Modified Gravity vs. Dark Energy

TL;DR

The paper proposes Minimal Modified Gravity (MMG), a model-independent parameterization using the gravitational growth index $\gamma$ to separate the effects of dark energy from modifications to gravity. By jointly fitting the expansion history and growth of structure, and employing Fisher-matrix forecasts for future weak lensing, supernova, and CMB data, the authors show that $\gamma$ can be constrained to about $\sigma(\gamma)\approx0.044$ (≈8% precision) when combining WL, SNe, and Planck, even while allowing for deviations from general relativity. Complementarity among probes reduces degeneracies with expansion parameters and neutrino mass, enabling discrimination between dark physics and physical darkness with only modest degradation in $w_0$ and $w_a$ constraints. The work also analyzes nonlinear regime concerns, proposing $k$-cutting and bias assessment strategies to balance information gain against model-systematic bias, and concludes that a balanced survey strategy leveraging both linear and quasi-linear scales is crucial for robust MG tests. Overall, the approach offers a practical route to testing beyond-Einstein gravity with upcoming cosmological surveys while maintaining strong leverage on the expansion history.

Abstract

The acceleration of the cosmic expansion may be due to a new component of physical energy density or a modification of physics itself. Mapping the expansion of cosmic scales and the growth of large scale structure in tandem can provide insights to distinguish between the two origins. Using Minimal Modified Gravity (MMG) - a single parameter gravitational growth index formalism to parameterize modified gravity theories - we examine the constraints that cosmological data can place on the nature of the new physics. For next generation measurements combining weak lensing, supernovae distances, and the cosmic microwave background we can extend the reach of physics to allow for fitting gravity simultaneously with the expansion equation of state, diluting the equation of state estimation by less than 25% relative to when general relativity is assumed, and determining the growth index to 8%. For weak lensing we examine the level of understanding needed of quasi- and nonlinear structure formation in modified gravity theories, and the trade off between stronger precision but greater susceptibility to bias as progressively more nonlinear information is used.

Figures (4)

• Figure 1: 68% and 95% CL constraints on the expansion history equation of state parameters $w_0$ and $w_a$, marginalized over all other parameters. The two blue (filled) contours give constraints from combining weak lensing, supernovae, cluster, and CMB data, while simultaneously fitting for beyond Einstein gravity. The black dot shows the fiducial model. The two red (empty) contours show the biased constraints if the modified gravity growth rate, here with $\Delta\gamma=0.1$, is ignored (i.e. fixing $\gamma$ to the general relativity value).
• Figure 2: 68% CL constraints on the gravitational growth index $\gamma$ and the matter density $\Omega_M$, marginalizing over the effective equation of state (and all other parameters). To fit for beyond Einstein gravity as well as the expansion history requires a combination of probes. Other effects on growth, such as neutrino masses, should be taken into account as well; the inner contour of each pair shows the effect of holding this fixed, most severe for weak lensing in isolation.
• Figure 3: Left panel: Cluster counts per $\Delta z=0.1$ as a function of redshift for our fiducial survey, for two values of the growth index ($\gamma=0.55$ and $0.65$). Also shown are cases when the equation of state and neutrino mass have been perturbed from their fiducial values by $0.05$ and $0.3$ eV respectively. Right panel: Auto-correlation power spectra of 4-bin weak lensing tomography for the two values of the growth index, with statistical errors shown for the $\gamma=0.55$ model.
• Figure 4: The solid (black) line shows the degradation in constraints on the growth index $\gamma$ from a SNAP-type weak lensing survey (plus SN+CMB) as small-scale weak lensing information is increasingly dropped. For each value of $k_{\rm cut}$, we drop all information from $k>k_{\rm cut}$ following nulling and compute the ratio of the constraint on $\gamma$ relative to the case when all information is used, that is, when $k_{\rm cut}=\infty$. The dashed curves (dark (red) and light (orange)) lines show the bias in the growth index divided by the $k_{\rm cut}=\infty$ statistical error for the bias model given in Eq. (\ref{['eq:SW_bias']}) with $c=0.05$ or $0.01$. The optimum choice of $k_{\rm cut}$, with the least risk, occurs near the intersection of the error and bias curves.