Indirect estimates of scalar-tensor modifications of the growth of structure at large scales

Resumen

An estimate to possible modifications to the growth of structure at very large scales according to cosmological observations different to direct measurements of LSS is derived. In order to do so, we construct and constrain the Effective Scalar-Tensor theory (EST) which arises as a phenomenological setup for modified theories of gravity as a first approximation in the very large scales limit where non-linearities are negligible. Estimates of the EST parameters are made using observations of the CMB and other complementary data which lead to an indirect determination of the rate of growth of LSS. It is assumed that the growth behaves as a general power law $\mu = \mu_0(1+r a^s)$ which is one-to-one mapped to an specific effective scalar-tensor theory defined by $\omega(a)=m\hspace{1mm}a^n$ where $m=1/2r\mu_0$ and $n=-s$. We derive a 1$\sigma$ constraint for the exponent $n=-0.47_{-0.47}^{+0.32}$ and $m=50.1\pm11.2$ or $m>3.2\times 10^3$ according to measurements of the CMB anisotropies from Planck and complementary data from BAO and HST. The result suggest two possible regimes where modifications of the growth may be detected in redshift surveys: 1) $\frac{\mu}{\mu_0}-1 < 6.2\times10^{-3}a^{0.47_{+0.47}^{-0.32}}$
and 2) $\frac{\mu}{\mu_0}-1 = 10^{-2}\pm0.089 \times a^{0.47_{+0.47}^{-0.32}}$.
%These results are valid as far as the phenomenological setup considered here is valid.