Observations of Type Ia supernovae suggest that the Universe has been accelerating since redshift z ∼ 0.5. Today the physical mechanism responsible for this process is still a mystery. The simplest model to explain the acceleration of the Universe is the ΛCDM model. This model assumes that the acceleration is driven by an exotic form of energy with negative pressure that might be related to the vacuum energy of quantum field theories. This theory is equivalent to adding an integration constant to the Einstein equations. Alternative theories to the vacuum energy, such as f(R) class of models propose a modification of gravity in the infrared that would produce an accelerated expansion. These models produce accelerated expansion through a modification of the Einstein-Hilbert action by an arbitrary function of the Ricci scalar R. As a consequence, an extra propagating scalar field appears that mediates a fifth force on all forms of matter.
In case the expansion of the Universe is driven by some of these alternative models, we expect that the growth of structure, namely f, to be different to the predictions from General Relativity. In order to detect such potential deviations in the growth of structure of the Universe, the redshift space power spectrum multipoles have been measured from galaxy spectroscopic surveys such as BOSS. One of the caveats of this technique is that at large scales the growth factor is fully degenerate with the amplitude of the linear dark matter power spectrum, and therefore only the quantity sigma8 times f can be constrained. Measuring the bispectrum allows to break this degeneracy, and therefore to obtain an isolated measurement of the growth of structure (and also sigma8) from galaxy surveys.
However, measuring the bispectrum from galaxy surveys and more importantly modelling its behaviour in redshift space for biased objects present several challenges that must be addressed if one wants to use this technique.
The aim of this talk is to talk about these challenges and limitations and present some possible solutions, focusing in the applicability of the method to galaxy surveys, with especial attention to BOSS.