Testing Gravity on Cosmological Scales
: Theoretical Predictions with the COLA Method

  • Bartolomeo Fiorini

Student thesis: Doctoral Thesis


The standard model of cosmology based on general relativity needs a dark energy component in the cosmic inventory to successfully describe the accelerated expansion of the universe at late time. This dark energy is not well justified by the standard model of particle physics. An alternative way to explain the accelerated expansion is to consider cosmological models based on modified gravity theories. The simplest extensions to general relativity include an additional scalar field mediating a fifth force. The gravity model is already well constrained with Solar System experiments, which show no sign of departure from general relativity in this environment. However, gravity still needs to be precisely constrained on cosmological scales. Among the modified gravity theories proposed in the literature, we focus on the ones which incorporate screening mechanisms, hiding the fifth force in high-density environments.
One of the main objectives of stage IV galaxy surveys is to constrain gravity on
cosmological scales but to fully take advantage of the constraining power of galaxy surveys it is important to formulate theoretical predictions in the non-linear regime of structure formation. This is possible by means of N-body simulations in combination with models for the galaxy-halo connection. However, full N-body simulations are computationally very expensive and modified gravity further increases their computational cost. In general relativity, approximate simulations method can be used to produce synthetic galaxy catalogues in place of full N-body simulations at the cost of reduced accuracy in the deep non-linear regime. One of these approximate methods, the so-called COLA (COmoving Lagrangian Acceleration) method, has been extended to simulate modified gravity theories.
In this context, we focus on two modified gravity theories, f (R) and nDGP (the
normal branch of the Dvali-Gabadadze-Porrati model), and develop a pipeline based on the COLA method to produce synthetic galaxy catalogues in modified gravity. By performing a comparison of COLA summary statistics with full N-body results, we validate each step of the pipeline and assess the accuracy of the COLA method. Our results show that COLA is able to accurately catch the modified gravity effect on the clustering of galaxies in redshift space, where traces of modified gravity are present in spite of the tuning of the free parameters of the galaxy-halo connection model. We then use the mock galaxy catalogues produced with our pipeline to study the effects of modified gravity and to validate COLA simulations for additional probes of the large-scale structures. These include an estimator of the power spectrum orthogonal to the line of sight Q0, the bispectrum and voids. Comparing Q0 with the real space power spectrum we show that the modified gravity signal contained in the two summary statistics is consistent and that COLA accurately reproduces the N-body results. In the bispectrum of dark matter instead, we find that COLA simulations, due to the screening approximation that they use, lack the modified gravity signal coming from the fifth force non-linearity in f (R) theory. Nonetheless, we show that this is not a problem for the monopole of bispectrum of galaxies in redshift space as this is dominated by non-linearities in the bias model, i.e., the model connecting dark matter with galaxies. We then look at how f (R) and nDGP theories affect the profiles of voids, finding more modified gravity signatures in nDGP than in f (R) theories. By applying a linear model for the redshift space distortions in voids we are able to recover unbiased estimates for the linear growth rate in all gravity theories, even when modified gravity is not taken into account in the redshift space distortion model. We also show that COLA results for voids are consistent with the N-body results.
While much faster than full N-body simulations, COLA simulations are still too
computationally expensive to be directly used for cosmological inference which
requires ∼ 105 evaluations of theoretical predictions. Here emulation techniques
come in help, requiring as little as ∼ 100 theoretical predictions to create smooth interpolating functions that cover a wide range of the theory parameter space. To pave the way in this direction, we study the convergence of COLA simulations for predictions of the matter power spectrum by increasing the force, time and mass resolutions employed in the simulations. We find that to achieve convergence it is necessary to increase the three resolutions accordingly. Then we explore the possibility of extending cosmological emulators with COLA simulations using the response function for the matter power spectrum, i.e., the response of the matter power spectrum to changes in cosmological parameters. By comparing COLA predictions of the response function with state-of-the-art cosmological emulators we show that COLA is more accurate in predicting the response function than the power spectrum itself. Finally, we demonstrate the potential of COLA simulations for the extension of cosmological emulators to modified gravity theories producing a suite of simulations in nDGP gravity that we employ to train an emulator for the modified gravity boost factor, i.e., the ratio of the power spectrum in modified gravity with that in general relativity.
The thesis is structured as follows:
• in chapter 1 we give a general overview of the main concepts at the base of
this work, including the cosmological model, modified gravity theories, the
large-scale structure of the universe and N-body simulations;
• in chapter 2 we present the pipeline for the efficient production of mock galaxy catalogues with the COLA method and validate it by performing an extensive comparison of summary statistics with full N-body simulations in modified gravity;
• in chapter 3 we test the validity of the COLA method for additional probes of
the large-scale structure, a real space power spectrum estimator, bispectrum
and voids, and investigate if they can help constrain modified gravity theories;
• in chapter 4 we study the feasibility of using COLA simulations to accurately
extend cosmological emulators of the matter power spectrum to modified
gravity theories and give an explicit example in the case of nDGP theory
producing an actual emulator;
• in chapter 5 we summarise the main results discussed in this thesis, draw the
conclusions and discuss future prospects.
Date of Award21 Feb 2023
Original languageEnglish
SupervisorKazuya Koyama (Supervisor), Albert Izard Alberich (Supervisor) & David Wands (Supervisor)

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