Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on the σ8 and H0 Tensions
Abstract
:1. Introduction
2. Running Vacuum in the Universe
3. Type I: Running Vacuum Interacting with Dark Matter
3.1. Background Equations
3.2. Perturbation Equations
3.3. Type I with Threshold
4. Type II: Running Vacuum with Running
4.1. Background Equations
Survey | z | Observable | Measurement | References |
---|---|---|---|---|
6dFGS+SDSS MGS | [Mpc] | [Mpc] | [125] | |
DR12 BOSS | 0.32 | [127] | ||
0.57 | ||||
WiggleZ | 0.44 | [Mpc] | [Mpc] | [126] |
0.60 | [Mpc] | [Mpc] | ||
0.73 | [Mpc] | [Mpc] | ||
DESY3 | [128] | |||
eBOSS Quasar | 1.48 | [129] | ||
Ly-Forests | [130] | |||
z | [km/s/Mpc] | References |
---|---|---|
[132] | ||
[133] | ||
[132] | ||
[134] | ||
0.1791 * | [135] | |
0.1993 * | [135] | |
[132] | ||
[134] | ||
[132] | ||
0.3519 * | [135] | |
0.3802 * | [136] | |
[134] | ||
0.4004 * | [136] | |
0.4247 * | [136] | |
0.4497 * | [136] | |
[137] | ||
0.4783 * | [136] | |
[138] | ||
0.5929 * | [135] | |
0.6797 * | [135] | |
[139] | ||
0.7812 * | [135] | |
0.8754 * | [135] | |
[138] | ||
[134] | ||
1.037 * | [135] | |
[134] | ||
1.363 * | [140] | |
[134] | ||
[134] | ||
[134] | ||
1.965 * | [140] |
4.2. Perturbation Equations
5. Data and Methodology
- Baseline: In our Baseline dataset, we consider the string SNIa+BAO++LSS+CMB. Note that here we do not include the SH0ES data.
- Baseline+SH0ES: The Baseline dataset is in this case complemented with the apparent magnitudes of the SNIa in the host galaxies and their distance moduli employed by SH0ES.
- Baseline (No pol.): The same as in the Baseline case, but now removing the high-ℓ polarization data from the CMB likelihood. That is to say, we have replaced the “CMB” dataset with “CMB (No pol.)”.
- Baseline (No pol.)+SH0ES: The same as in “Baseline (No pol.)”, but including also the data from SH0ES.
Baseline | |||||
---|---|---|---|---|---|
Parameter | CDM | Type-I RRVM | Type-I RRVMthr. | Type-II RRVM | XCDM |
(km/s/Mpc) | |||||
- | - | ||||
- | - | - | - | ||
- | - | - | - | ||
M | |||||
(Mpc) | |||||
- | −2.04 | +15.34 | −4.18 |
Baseline +SH0ES | |||||
---|---|---|---|---|---|
Parameter | CDM | Type-I RRVM | Type-I RRVMthr. | Type-II RRVM | XCDM |
(km/s/Mpc) | |||||
- | - | ||||
- | - | - | - | ||
- | - | - | - | ||
M | |||||
(Mpc) | |||||
- |
Baseline (No pol.) | |||||
---|---|---|---|---|---|
Parameter | CDM | Type-I RRVM | Type-I RRVMthr. | Type-II RRVM | XCDM |
(km/s/Mpc) | |||||
- | - | ||||
- | - | - | - | ||
- | - | - | - | ||
M | |||||
(Mpc) | |||||
- |
Baseline (No pol.) +SH0ES | |||||
---|---|---|---|---|---|
Parameter | CDM | Type-I RRVM | Type-I RRVMthr. | Type-II RRVM | XCDM |
(km/s/Mpc) | |||||
- | - | ||||
- | - | - | - | ||
- | - | - | - | ||
M | |||||
(Mpc) | |||||
- |
6. Discussion of the Results
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Additional Tables
Baseline | |||||
---|---|---|---|---|---|
Experiment | CDM | Type-I RRVM | Type-I RRVMthr. | Type-II RRVM | XCDM |
CMB | |||||
SNIa | |||||
BAO- (correl.) | |||||
BAO | |||||
Baseline+SH0ES | |||||
---|---|---|---|---|---|
Experiment | CDM | Type-I RRVM | Type-I RRVMthr. | Type-II RRVM | XCDM |
CMB | |||||
SNIa | |||||
BAO- (correl.) | |||||
BAO | |||||
Baseline (No pol.) | |||||
---|---|---|---|---|---|
Experiment | CDM | Type-I RRVM | Type-I RRVMthr. | Type-II RRVM | XCDM |
CMB | |||||
SNIa | |||||
BAO- (correl.) | |||||
BAO | |||||
1 | https://lesgourg.github.io/class_public/class.html, accessed on 22 May 2023. |
2 | In practice this means that we have first fitted the value of as one more free parameter in our analysis. Subsequently, we have assumed that the threshold point remains fixed at that point; see also [107,108,109,110] for a binned/tomographic approach to the DE. In our case, we have just one threshold whose existence might be motivated by QFT calculations [30,31]. |
3 | If (dark) matter is not conserved but G remains constant, we retrieve of course our previous scenario (16). In general, we may expect a mixture of both situations, but we shall refrain from dealing with the general case since it would introduce extra parameters; see, however, [111,112] for additional discussions that can be relevant for studies on the possible variation in the fundamental constants of nature. |
4 | It should be clear that is not a dynamical degree of freedom, in contradistinction to Brans–Dicke-type theories of gravitation [113], and therefore does not mediate any sort of long-range interaction that should be subdued by screening mechanisms. |
5 | Let us emphasize that Equation (56) is valid only in the MDE, and we have also pointed out that const. in the DE epoch. This means that G becomes more and more rigid when it transits from the MDE to the DE epoch, and therefore the actual limits on are weaker than those that we have roughly estimated. This works to our benefit of course. In fact, a detailed calculation would require computing in the DE epoch, but it proves unnecessary once we have shown that even in the most unfavorable case (i.e., when evolves more rapidly than it actually does in the DE epoch) the obtained limits on are nonetheless preserved by our fits. Notice that type-I models are totally unaffected by these limits, since G is in this case constant, so can be, in principle, larger for them. |
6 | https://gitlab.com/mmoresco/CCcovariance/-/blob/master/examples/CC_covariance.ipynb, accessed on 22 May 2023. |
7 | While it is common to rescale the measured values of by a factor to account for the Alcock–Paczynski (AP) effect [157] (in which the tildes denote the quantities computed in the fiducial cosmology employed by the galaxy surveys), there does not not seem to exist a general consensus on the exact correction to apply; see, e.g., [158] and references therein. In this sense, the above formula should be considered as just a rough estimate. We have checked that the AP-rescaling introduces negligible shifts in our fitting results, a conclusion that is well in accordance with previous analyses in the literature [38,39,158]. For this reason, we have opted to not include this correction in our work. |
8 | This region is also preferred by late-time dynamical DE models when fitted to a very wide variety of background data that are independent from the direct cosmic distance ladder and CMB, km/s/Mpc [161]. See [162,163,164,165] for measurements of more in accordance with SH0ES obtained also with the tip of the red giant branch method. |
9 | https://baudren.github.io/montepython.html, accessed on 22 May 2023. |
10 | https://getdist.readthedocs.io/en/latest/, accessed on 22 May 2023. |
11 | See Section 3.3 for the practical implementation. |
12 | |
13 | |
14 | Noticeably, the central values of , , and the absolute magnitude of SNIa, M, obtained for the type-II RRVM when the CMB polarization data are excluded in the fitting analysis are in very good agreement with the model-independent measurements from low-z data reported in [152], which are also independent from the main drivers of the tension. For the Hubble constant, these authors find km/s/Mpc. However, these measurements still have large uncertainties and cannot arbitrate the Hubble tension yet; see also [179]. |
15 |
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Solà Peracaula, J.; Gómez-Valent, A.; de Cruz Pérez, J.; Moreno-Pulido, C. Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on the σ8 and H0 Tensions. Universe 2023, 9, 262. https://doi.org/10.3390/universe9060262
Solà Peracaula J, Gómez-Valent A, de Cruz Pérez J, Moreno-Pulido C. Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on the σ8 and H0 Tensions. Universe. 2023; 9(6):262. https://doi.org/10.3390/universe9060262
Chicago/Turabian StyleSolà Peracaula, Joan, Adrià Gómez-Valent, Javier de Cruz Pérez, and Cristian Moreno-Pulido. 2023. "Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on the σ8 and H0 Tensions" Universe 9, no. 6: 262. https://doi.org/10.3390/universe9060262