Weak gravity on a ΛCDM background

We consider Horndeski modified gravity models obeying stability, velocity of gravitational waves c(T) equals c and quasistatic approximation on subhorizon scales. We assume further a Lambda cold dark matter background expansion and a monotonic evolution on the cosmic background of the alpha functions as alpha(i) = alpha(i0)a(s) where i = M, B, a is the scale factor and alpha(i0) (alpha(M0), alpha(B0)), s are arbitrary parameters. We show that the growth and lensing reduced (dimensionless) gravitational couplings mu G(growth)/G, Sigma G(lensing)/Gexhibit the following generic properties today: Sigma(0) < 1 for all viable parameters, mu(0) < 1 (weak gravity today) is favored for small s while mu(o) > 1 is favored for large s. We establish also the relation mu >= Sigma at all times. Taking into account the f sigma(8) and E-G data we constrain the parameter s to satisfy s less than or similar to 2. Hence these data select essentially the weak gravity regime today (mu(0) < 1) when s < 2, while mu(0) > 1 subsists only marginally for s approximate to 2. At least the interval 0.5 less than or similar to s less than or similar to 2 would be ruled out in the absence of screening. We consider further the growth index gamma(z) and identify the (alpha(M0), alpha(B0)) parameter region that corresponds to specific signs of the differences gamma(0) - gamma(Lambda CDM)(0), and gamma(1) - gamma(Lambda CDM)(1), where gamma(0) vertical bar(z=0) and gamma(1) dy/dz vertical bar(z=0). In this way important information is gained on the past evolution of mu. We obtain in particular the signature gamma(0) > gamma(Lambda CDM)(0) for s < 2 in the selected weak gravity region.

Automated summary

The study focuses on Horndeski modified gravity models fulfilling stability and gravitational wave speed conditions, with a further assumption of the evolution of cosmic alpha functions in a Lambda cold dark matter background. It is found that the gravitational couplings display specific properties based on various parameters, with a preference for weak gravity today and certain limits on the parameter s. The analysis also considers the growth index gamma(z) to gain insights into the past evolution of mu, revealing important information on the dynamics of gravity in different scenarios.