#
Probing Inflation with Large-Scale Structure Data: The Contribution of Information at Small Scales^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

- The nature of dark matter, which constitutes the bulk of the matter content.
- The component causing the accelerated expansion of the Universe. This may be a cosmological constant ($\Lambda $, or some additional component known as dark energy, which may be dynamical, with a redshift-dependent equation of state (parametrized by some expression for w, e.g., $w={w}_{0}+{w}_{a}(1-a)$ or it may be a constant.
- Conditions in the very early Universe. The Theory of Inflation is well-established, and has been confirmed with remarkable precision by a succession of cosmic microwave background (CMB) probes. WMAP [1,2] provided conclusive evidence for inflation. Planck [3,4] conclusively excluded a scale-invariant primordial power spectrum. What is the form of this power spectrum beyond its main shape and amplitude? Does it contain features? If so, at which scales do they occur? What is the inflaton potential producing this power spectrum?

## 2. Primordial Physics

#### The Inflationary Potential

## 3. Method

- Simulated Planck CMB data alone (shown in red in the triangle plots);
- Joint Euclid Conservative galaxy clustering + Euclid Conservative cosmic shear + simulated Planck CMB data (shown in blue);
- Joint Euclid Realistic galaxy clustering + Euclid Realistic cosmic shear + simulated Planck CMB data (shown in green).

#### 3.1. The Non-Linear Theoretical Uncertainty: ‘Conservative’ and ‘Realistic’ Setups

- Conservative galaxy clustering: We use a cut-off on large wavelengths at ${k}_{\mathrm{min}}=0.02\phantom{\rule{3.33333pt}{0ex}}{\mathrm{Mpc}}^{-1}$. This eliminates scales which are bigger than the bin width or which violate the small-angle approximation. On small wavelengths, we use a theoretical uncertainty with ${k}_{\mathrm{NL}}\left(0\right)=0.2h\phantom{\rule{0.166667em}{0ex}}{\mathrm{Mpc}}^{-1}$.
- Realistic galaxy clustering: The same formulation, but with ${k}_{\mathrm{max}}=10h\phantom{\rule{0.166667em}{0ex}}{\mathrm{Mpc}}^{-1}$

- Conservative cosmic shear: We include multipoles from ${\ell}_{\mathrm{min}}=5$ up to a bin-dependent non-linear cut-off given by ${k}_{\mathrm{NL}}\left(0\right)=0.5h\phantom{\rule{0.166667em}{0ex}}{\mathrm{Mpc}}^{-1}$
- Realistic cosmic shear: the same, but with ${k}_{\mathrm{NL}}\left(0\right)=2h\phantom{\rule{0.166667em}{0ex}}{\mathrm{Mpc}}^{-1}$.

#### 3.2. Fiducial Cosmology and WWI Models

## 4. Results

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CMB | Cosmic microwave background |

$\Lambda $CDM | $\Lambda $ cold dark matter |

MCMC | Markov chain Monte Carlo |

WMAP | Wilkinson Microwave Anisotropy Probe |

WWI | Wiggly Whipped Inflation |

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**Figure 1.**One-dimensional posteriors and marginalized contours ($1\sigma $ and $2\sigma $) for the inflation parameters in the WWI: Featureless model. The addition of Euclid data results in a significant improvement in constraints for the amplitude parameter, and there is only slight improvement with Euclid Realistic compared to Euclid Conservative.

**Figure 2.**One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–A model. Improvement in the constraints is most evident in the amplitude parameter ${V}_{0}$. The constraints from Euclid Realistic are slightly better than Euclid Conservative.

**Figure 3.**One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–B model. There is significant improvement in constraints for all inflation parameters with the addition of Euclid data, but little difference between Euclid Conservative and Realistic.

**Figure 4.**One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–C model. As with WWW–A, there is some improvement when Euclid Realistic is used.

**Figure 5.**One-dimensional posteriors and marginalized contours for the inflation parameters in the WWI–D model. We note a significant improvement from Euclid Realistic over Euclid Conservative for all parameters.

**Figure 6.**One-dimensional posteriors and marginalized contours for the inflation parameters in the WWIP: Featureless model. Euclid Realistic shows some improvement over Euclid Conservative.

**Figure 7.**One-dimensional posteriors and marginalized contours for the inflation parameters in the WWIP: Planck-best-fit model. Again, Euclid Realistic shows some improvement over Euclid Conservative.

**Figure 8.**One-dimensional posteriors and marginalized contours for the inflation parameters in the WWIP: Small-scale-feature model. We obtain closed contours for all the inflation parameters, with a significant improvement with Euclid data are added. Euclid Realistic provides further improvement.

**Table 1.**Parameter values for the inflationary potential parameters used to obtain the fiducial primordial power spectra.

Model | $ln\left({10}^{10}{\mathit{V}}_{0}\right)$ | ${\mathit{\varphi}}_{0}$ | $\mathit{\gamma}$ | ${\mathit{\varphi}}_{\mathbf{T}}$ | $ln\mathit{\delta}$ |
---|---|---|---|---|---|

WWI: Featureless | $1.73$ | 0 | 0 | – | – |

WWI–A | $1.73$ | $0.0137$ | $0.019$ | $7.89$ | $-4.5$ |

WWI–B | $1.75$ | $0.0038$ | $0.04$ | $7.91$ | $-7.1$ |

WWI–C | $1.72$ | $0.0058$ | $0.02$ | $7.91$ | $-6$ |

WWI–D | $1.76$ | $0.003$ | $0.033$ | $7.91$ | $-11$ |

WWIP: Featureless | $0.282$ | 0 | – | – | – |

WWIP: Planck-best-fit | $0.282$ | $0.11$ | – | $4.51$ | – |

WWIP: Small-scale-feature | $0.3$ | $0.18$ | – | $4.5$ | – |

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**MDPI and ACS Style**

Debono, I.
Probing Inflation with Large-Scale Structure Data: The Contribution of Information at Small Scales. *Phys. Sci. Forum* **2021**, *2*, 45.
https://doi.org/10.3390/ECU2021-09371

**AMA Style**

Debono I.
Probing Inflation with Large-Scale Structure Data: The Contribution of Information at Small Scales. *Physical Sciences Forum*. 2021; 2(1):45.
https://doi.org/10.3390/ECU2021-09371

**Chicago/Turabian Style**

Debono, Ivan.
2021. "Probing Inflation with Large-Scale Structure Data: The Contribution of Information at Small Scales" *Physical Sciences Forum* 2, no. 1: 45.
https://doi.org/10.3390/ECU2021-09371