# Is the Hubble Crisis Connected with the Extinction of Dinosaurs?

## Abstract

**:**

## 1. Introduction

- The sound horizon scale is properly calibrated by the CMB anisotropy spectrum and/or BBN in the context of standard prerecombination physics.
- The form of $E\left(z\right)$ is consistent with (1) as constrained by low z distance probes which are independent of any type of calibration.
- The calibration of SnIa implemented e.g., via Cepheid stars at $z<0.01$ remains valid at $z>0.01$ where the Hubble flow is probed.

#### 1.1. Gravitational Transition as a Proposed Solution to the Hubble Crisis

- They have the same good quality of fit as the standard $\Lambda $CDM for geometric cosmological data that probe the Hubble expansion rate $H\left(z\right)$ while being consistent with local calibrators (e.g., Cepheid stars) of the SnIa absolute magnitude [20].
- They have better quality of fit than standard $\Lambda $CDM for dynamical cosmological data that probe the growth rate of cosmological perturbations (weak lensing [52,53,54], redshift space distortions [55,56,57] and cluster count data [58,59,60,61,62,63]). These data suggest weaker growth than that implied by $\Lambda $CDM in the context of general relativity [64,65,66,67]. This weaker growth is naturally provided in the context of the gravitational transition to weaker gravity (lower ${G}_{\mathrm{eff}}$) at early times assumed in this class of models [19].
- The sudden gravitational transition hypothesis has several profound observational consequences that make it testable by a wide range of data on scales starting from geological and solar system scales up to astrophysical and cosmological scales. Surprisingly, current data can not rule out such gravitational transition because only the time derivative of ${G}_{\mathrm{eff}}$ is strongly constrained while constraints on a transition are much weaker (see Table 1). Instead, hints have recently been found for such a transition in Tully–Fisher data [30] and also in Cepheid-SnIa calibrator data [50].

#### 1.2. Observational Constraints on the Gravitational Transition

#### 1.3. Effects of a Gravitational Transition on the Solar System Chronology

## 2. The Oort Cloud and Long Period Comets

## 3. Effects of a Gravitational Transition on the LPC Flux: A Monte Carlo Approach

- We consider a sample of $N={10}^{5}$ points (LPCs) with random initial radial coordinate distances ${r}_{i}$ from the primary focus of the ellipse ranging from ${10}^{4}\phantom{\rule{3.33333pt}{0ex}}\mathrm{AU}$ to $4\times {10}^{4}\phantom{\rule{3.33333pt}{0ex}}\mathrm{AU}$, with initial velocity corresponding to circular orbits perturbed by a random velocity perturbation, and with random magnitude ${v}_{r}$ ranging from 0 to $0.14$ AU/yr and direction ${\theta}_{r}$. The corresponding unperturbed circular velocities ${v}_{c}=\sqrt{4{\pi}^{2}/{r}_{i}}$ range from ${v}_{c}=0.03$ AU/yr to ${v}_{c}=0.06$ AU/yr. Thus, the considered velocity perturbations are of the same order as the unperturbed initial circular velocities and are assumed to be induced by stellar encounters and/or by galactic tidal effects.
- The total initial velocities of each simulated comet in polar coordinates are obtained from a superposition of the unperturbed initial circular velocity plus a random velocity perturbation,$$\begin{array}{cc}\hfill {v}_{x}^{i}& ={v}_{r}cos{\theta}_{r}-\sqrt{\frac{4{\pi}^{2}}{{r}_{i}}}sin{\theta}_{i}\hfill \end{array}$$$$\begin{array}{cc}\hfill {v}_{y}^{i}& ={v}_{r}sin{\theta}_{r}+\sqrt{\frac{4{\pi}^{2}}{{r}_{i}}}cos{\theta}_{i}\hfill \end{array}$$
- From comets with the randomly perturbed velocities, we then select those that have the following properties: a. their semi-major axis as obtained from (10) is in the range $\alpha \in [{10}^{4},4\times {10}^{4}]\phantom{\rule{3.33333pt}{0ex}}\mathrm{AU}$ and b. their eccentricity after the perturbation is inside the loss cone, namely they have a perihelion p less than ${p}_{*}=10\phantom{\rule{3.33333pt}{0ex}}\mathrm{AU}$ (approximately Saturn’s distance from the Sun). This condition corresponds to eccentricities in the range ${e}^{2}\in [1-2{p}_{*}/\alpha ,1]$ [83]. This implies that these perturbed comets will enter the solar system and suffer stronger perturbations by the solar system planets, which could thus further disrupt their orbits, leading to possible impacts with planets or satellites in the solar system. The percentage of comets that enter the planetary region is thus recorded for various ranges of the velocity perturbation magnitude ${v}_{r}$.
- The above Monte Carlo simulation is repeated for a $10\%$ increased value of Newton’s constant ${G}_{\mathrm{eff}}$, which corresponds to increasing the value of $\mu $ (or the value $4{\pi}^{2}$ by which $\mu $ is replaced in the AU-yr units) by the same percentage. The new fraction of comets that enter the loss cone (planetary region) is thus recorded, and its ratio is taken over the corresponding fraction obtained with the standard value of $\mu $ ($4{\pi}^{2}$). This ratio provides the excess probability that the comet will enter the loss cone after the gravitational transition to stronger gravity.

## 4. Conclusions

- The new extended Pantheon + dataset [2] of Cepheid + SnIa data provides the opportunity for a comprehensive analysis of the unified Cepheid+SnIa data in the redshift range $z\in [0,2.3]$ in a self-consistent and unified manner. Such an analysis which may be implemented once the full Pantheon+ dataset becomes publicly available will allow the more detailed search for signatures of a transition for redshifts $z\lesssim 0.01$, extending the analysis of [50]. Even in the current analysis of the Pantheon + dataset [2], hints for a transition are evident in Figure 10 of [2], where it is shown that the more distant Cepheids in SnIa hosts tend to have a higher value of the period luminosity parameter than the Cepheids in the closeby anchor galaxies (Figure 7). This effect is significantly amplified if the outliers are taken into account (red points).
- As implied by Equation (5), the temperature of Earth strongly depends on the value of ${G}_{\mathrm{eff}}$ (see Equation (5)) [70] and so does the solar luminosity $\mathcal{L}\sim {G}_{\mathrm{eff}}^{7}{M}_{\odot}^{5}$. Thus, an increase in ${G}_{\mathrm{eff}}$ would lead to a similar increase in the Earth temperature. Thus, a careful search of unaccounted for temperature variations of Earth during the past $150\phantom{\rule{3.33333pt}{0ex}}\mathrm{Myrs}$ could either impose strong constraints on the gravitational transition hypothesis, or could reveal possible signatures of such an event.
- The search for physically motivated models and mechanisms that could generically predict the presence of such a gravitational transition realized either spatially through the nucleation of true vacuum bubbles [50] or as a transition in time involving, e.g., a pressure singularity [68], is also an interesting extension of this analysis.
- The study of the stability of the whole solar system under a gravitational transition is also an interesting extension of the present analysis. The Lyapunov time of the chaotic solar system is of O (100 Myrs). Therefore, it is highly nontrivial to conclude that the solar system is stable or unstable under a finite transition of ${G}_{\mathrm{eff}}$ on the timescale of the Lyapunov time. The question to address in this context is ‘What is the maximum abrupt fractional change of ${G}_{\mathrm{eff}}$ such that the solar system survives the transition?’. For a two body Sun–Earth system, it is easy to show via a simple simulation that the orbit of the Earth gets slightly deformed by an abrupt $10\%$ change in the gravitational strength, but this cannot be generalized to the much more complex full solar system dynamics.

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Note

1 | It has been shown by [18] that gravitational transitions with high ${z}_{t}$ are unable to resolve the cosmological tensions. |

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**Figure 1.**The deep ocean temperatures versus time, extended over a range of epochs from the Paleocene to the Pliocene. The temperatures in the distant past were calculated using oxygen isotope ratios from fossil foraminifera (one-celled protists, eukaryotic organisms), while the red part of the plot assumes an ice-free ocean and the gray part does not. A thermal maximum approximately 55 Myrs ago is clearly seen. The graph is by Hunter Allen and Michon Scott, using data from the NOAA National Climatic Data Center, courtesy of Carrie Morrill. For details see https://www.climate.gov/news-features/features/models-and-fossils-face-over-one-hottest-periods-earths-history (accessed on 20 March 2022).

**Figure 2.**The definition of the semi-major axis $\left(\alpha \right)$, eccentricity (e), the primary focus and the distance from the primary focus (r) of an ellipse.

**Figure 3.**The cyan points correspond to the ratio of the probability for comets to enter our Solar system after the $10\%$ gravitational transition, over the same probability before the transition, for different values of random initial velocity perturbations (${v}_{mean}$) on the initial comet velocity. The red line corresponds to a non linear fit of the numerical results in the form of an exponential function.

**Figure 4.**The eccentricity versus the semi major axis plots of the comets constructed in the Monte Carlo simulations for velocity perturbation magnitude in the range between $0.1$ and $0.14$. The red points correspond to the comets whose elliptic trajectories remain outside the planetary region after the velocity perturbation, whereas the green points correspond to those that enter the planetary region after the velocity perturbation. Left panel: The perturbed comet orbit parameters before the gravitational transition. Right panel: The perturbed comet orbit parameters after the gravitational transition has occurred, increasing the gravitational strength $\mu $ by $10\%$. Notice the significant increase in the number of comets that enter the solar system.

**Figure 5.**The velocity perturbation magnitude vs the initial position plots of the comets in the Monte Carlo simulations that are initially in stable orbits staying at perihelion distance larger than $10\phantom{\rule{3.33333pt}{0ex}}\mathrm{AU}$. The orange points correspond to the comets whose elliptic trajectories remain outside the solar system despite the velocity perturbation, whereas the blue points correspond to those that enter our solar system after the same initial velocity perturbation. Left panel: The comet initial phase space coordinates before the gravitational transition. Right panel: The comet initial phase space coordinates after the gravitational transition has occurred, increasing the gravitational strength $\mu $ by $10\%$. Notice the significant increase in the number of comets that enter the solar system.

**Figure 6.**Left panel: The 2D scatter plot of the positions of the collection of points used in the Monte Carlo analysis (excluding those that evolve to parabolic trajectories), colored by the value of their individual velocity before the gravitational transition. Right panel: The 2D scatter plot of the positions of the points used in the Monte Carlo process, maintaining elliptic orbits, colored by the value of their individual velocity after the gravitational transition. The increased initial velocity is due to the increased gravitational strength, which requires higher velocity for an initial circular unperturbed orbit.

**Figure 7.**The period-luminosity parameter for the Cepheids in anchor galaxies and in SnIa host galaxies (Figure 10 from Ref. [2]). The trend for most SnIa hosts (more distant galaxies) for a higher value of the Cepheid period-luminosity parameter (${m}_{H}^{W}$ slope) compared to nearby galaxies (MW, LMC, SMC, N4258 and M31) is evident. This trend is even stronger if the outliers are also included in the sample (red points).

**Table 1.**Solar system, astrophysical and cosmological constraints on the evolution of the gravitational constant. Methods with star (∗) constrain ${G}_{*}$ (connected with the Planck mass) while the rest constrain ${G}_{\mathrm{eff}}$. The latest and strongest constraints are shown for each method (updated from Ref. [30]).

Method | $|\frac{\mathit{\Delta}{\mathit{G}}_{\mathbf{eff}}}{{\mathit{G}}_{\mathbf{eff}}}{|}_{\mathit{max}}$ | $|\frac{{\dot{\mathit{G}}}_{\mathbf{eff}}}{{\mathit{G}}_{\mathbf{eff}}}{|}_{\mathit{max}}$ (${\mathbf{yr}}^{-1}$) | Time Scale (yr) | References |
---|---|---|---|---|

Lunar ranging | $1.47\times {10}^{-13}$ | 24 | [31] | |

Solar system | $4.6\times {10}^{-14}$ | 50 | [32] | |

Pulsar timing | $3.1\times {10}^{-12}$ | 1.5 | [33] | |

Orbits of binary pulsar | $1.0\times {10}^{-12}$ | 22 | [34] | |

Ephemeris of Mercury | $4\times {10}^{-14}$ | 7 | [35] | |

Exoplanetary motion | ${10}^{-6}$ | 4 | [36] | |

Hubble diagram SnIa | 0.1 | $1\times {10}^{-11}$ | ∼${10}^{8}$ | [27] |

Pulsating white-dwarfs | $1.8\times {10}^{-10}$ | 0 | [37] | |

Viking lander ranging | $4\times {10}^{-12}$ | 6 | [38] | |

Helioseismology | $1.6\times {10}^{-12}$ | $4\times {10}^{9}$ | [39] | |

Asteroseismology | $1.2\times {10}^{-12}$ | $1.1\times {10}^{10}$ | [40] | |

Gravitational waves | 8 | $5\times {10}^{-8}$ | $1.3\times {10}^{8}$ | [41] |

Paleontology | $0.1$ | $2\times {10}^{-11}$ | $4\times {10}^{9}$ | [26] |

Globular clusters | $35\times {10}^{-12}$ | ∼${10}^{10}$ | [42] | |

Binary pulsar masses | $4.8\times {10}^{-12}$ | ∼${10}^{10}$ | [43] | |

Gravitochemical heating | $4\times {10}^{-12}$ | ∼${10}^{8}$ | [44] | |

Strong lensing | $3\times {10}^{-1}$ | ∼${10}^{10}$ | [45] | |

Big Bang Nucleosynthesis ${}^{*}$ | $0.05$ | $4.5\times {10}^{-12}$ | $1.4\times {10}^{10}$ | [28] |

Anisotropies in CMB ${}^{*}$ | $0.095$ | ${10}^{-13}$ | $1.4\times {10}^{10}$ | [46,47,48] |

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Perivolaropoulos, L.
Is the Hubble Crisis Connected with the Extinction of Dinosaurs? *Universe* **2022**, *8*, 263.
https://doi.org/10.3390/universe8050263

**AMA Style**

Perivolaropoulos L.
Is the Hubble Crisis Connected with the Extinction of Dinosaurs? *Universe*. 2022; 8(5):263.
https://doi.org/10.3390/universe8050263

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2022. "Is the Hubble Crisis Connected with the Extinction of Dinosaurs?" *Universe* 8, no. 5: 263.
https://doi.org/10.3390/universe8050263