# Constraining the Swiss-Cheese IR-Fixed Point Cosmology with Cosmic Expansion

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## Abstract

**:**

## 1. Introduction

## 2. Swiss-Cheese Model and IR-Fixed Point Cosmology

#### 2.1. Asymptotic Safety in UV and IR

#### 2.2. AS Swiss-Cheese

#### 2.3. Cosmic Acceleration and Coincidence Problem

## 3. Methodology and Numerical Results

^{−1}Mpc

^{−1}adapted from the latest CMB inferred constraints from the Planck collaboration [57] while dark energy equation of state parameters are motivated from the baseline fiducial values of SNe Ia observations.

^{−1}Mpc

^{−1}. A detailed plot of the ${H}_{0}$ permissible range as a function of the b values is shown in Figure 3.

#### 3.1. b Constraint from ${w}_{DE,0}$ and ${H}_{0}$ Combination

#### 3.2. Observational Hubble Data

#### 3.3. Matching at the Galaxy 0 Scale

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**Up**): Comparison of $H\left(z\right)$ between $\Lambda $CDM values and our model’s values with best fit value of $b=1.505$ and for $b=2.08$, which corresponds to the maximum value of b for the residual error as ≤1%. The error bars in the residue plot panel (and the grey highlighted zone), correspond to the standard deviation in the respective redshift bin, computed from all the b values mentioned in the main text. (

**Down**): The same comparison, but for $b=2.11$, which corresponds to the error limit of ≤5%. The bottom panel in both the plots shows the corresponding residual plot.

**Figure 2.**(

**Up**): 1% error. (

**Down**): 5% error limit. The red line shows the error percentage against the b value. The blue dashed horizontal line marks the two corresponding levels of error margin. The grey shaded region marks the allowed range of b values for which the error level will be either ≤1% or ≤5%. The horizontal black dashed line marks the maximum limit of the b value. The thick black horizontal line shows the best fit b value.

**Figure 3.**(

**Up**): Value of ${H}_{0}$ plotted against the current day ${w}_{DE}$ values for a family of b values. The lines are demarcated into two broad groups, one $b<1.54$ (coloured lines) the other $b>1.54$ (grey tone lines), separated by the $b=1.54$ line, shown in broad black dashed line, which corresponds to the best fit b value. (

**Down**): A zoomed in plot of the left figure. The corresponding grey toned lines (for $b>1.54$ case) are shown in green tone lines here. We observed that, for low b values, the evolution of the Hubble constant value at the present time had a minimum correlation to the current dark energy parameter constraint. As b is increased, the tilt in the ${H}_{0}-{w}_{DE,0}$ relation increases toward a more positive correlation. The blue vertical dashed line marks the ${w}_{DE,0}$ value from our model. For very low values of b or for $b>2.065$, the ${H}_{0}$ values come closest to the current observed ${H}_{0}=67.5$ km/s/Mpc value.

**Figure 4.**Residual plot of $\Delta {H}_{0}$ computed from the difference of 67.5 km/s/Mpc and ${H}_{0}$ computed at $z=0,{w}_{DE,0}=-0.95$ from Equation (17) for a family of ‘b’ values. As seen, the red dot corresponding to $b\simeq 2.07$ marks the point of the lowest residual. The blue and the red dashed horizontal lines mark the $1\%$ and $5\%$ error levels and their corresponding b values.

**Figure 5.**Plot showing the ratio between the Hubble parameter (H(z)) from our Swiss-cheese model computed at the best fit value of $b=2.065$ and the Hubble parameter corresponding to the LCDM model for the redshift ranges of z = [0–2.4].

**Figure 6.**Plot of the best fit Hubble parameter value of our Swiss-cheese model, $H(z,\phantom{\rule{4pt}{0ex}}b=2.065)$ (green dashed) against the redshift binned OHD with their corresponding error bars (red) for z = [0–2.4]. The yellow margin represents the extent of the $H(z,b)$ values of our model when b is varied between 0.01–3.0 across the full redshift range. The bottom plot shows the ratio of the error between the OHD data (red in top panel) and the best fit Swiss-cheese data (green in top panel), i.e., $\delta \left(H\right)$ and the Hubble parameter (green dots). The gray-shaded margin corresponds to the mean error level (∼0.07).

**Table 1.**The upper limit of b for the corresponding permissible error margin computed from the Hubble parameter estimates and Hubble constant and ${w}_{DE,0}$ combined constraint.

Error % | b (from H(z)) | b (from H_{0} + w_{DE,0}) |
---|---|---|

1 | 2.08 | 2.07 |

5 | 2.11 | 2.08 |

**Table 2.**The same as in Table 1 but with the galaxy-based Swiss-cheese model.

Error % | b (from H(z)) | b (from H_{0} + w_{DE,0}) |
---|---|---|

1 | 2.13 | 2.11 |

5 | 2.16 | 2.13 |

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**MDPI and ACS Style**

Mitra, A.; Zarikas, V.; Bonanno, A.; Good, M.; Güdekli, E.
Constraining the Swiss-Cheese IR-Fixed Point Cosmology with Cosmic Expansion. *Universe* **2021**, *7*, 263.
https://doi.org/10.3390/universe7080263

**AMA Style**

Mitra A, Zarikas V, Bonanno A, Good M, Güdekli E.
Constraining the Swiss-Cheese IR-Fixed Point Cosmology with Cosmic Expansion. *Universe*. 2021; 7(8):263.
https://doi.org/10.3390/universe7080263

**Chicago/Turabian Style**

Mitra, Ayan, Vasilios Zarikas, Alfio Bonanno, Michael Good, and Ertan Güdekli.
2021. "Constraining the Swiss-Cheese IR-Fixed Point Cosmology with Cosmic Expansion" *Universe* 7, no. 8: 263.
https://doi.org/10.3390/universe7080263