The fiducial cosmological model posits the existence of a non-zero value of the “cosmological constant.” Some questions from easiest to hardest: What is the cosmological constant?
I explained the Pantheon Supernova Observations using my epoch-dependent G model. The model has just two parameters: the 4D radius of the Universe and the G**(-alpha) dependence of the Absolute Luminosity of SN1a. I derived that to be alpha=3.0. That makes all photometric distances to be overestimated by G**(1.5). In HU G= G0 * (1+z) so, all distances are overestimated by (1+z)**1.5
Once you correct the distances, HU predicts the photometric distance with D(z) = R0 * z/(1+z)
where R0 = 14.5 GLY and H0 = 67.5 km/s/Mpc
That matches the CMB H0 and thus there is no Crisis In Cosmology left.
Of course, I also refuted NASA Laser Lunar Ranging analysis and SN1a based G-variability papers. They are of poor quality and made basic mistakes. SN1a papers keep the Stellar Candles Hypothesis (which is the same as the constant G hypothesis) and try to ascertain G variability. NASA has used the G-Constant determined Earth moment of inertia when trying to evaluate G-variability.
Those are basic mistakes.
Earth Temperature History was explained by having the Sun being born as a binary (0.3:0.7). The initial mass distribution was defined by the early Earth Temperature. The time of merger was defined by the current core isotope composition. I modified MESA code to accommodate variable G. When the Sun was born, G was 1.47 G0 (where G0 is the current value of G).
In other words, I created a better model than L-CDM (1 parameter instead of seven), debunked constraints on G variability. The only problem I have is that journal editors will simply reject my work without providing a single reason or a peer review.
Of course, my work also predicted all planets' and binary pulsars' precession and derived the SSB Reference Frame Absolute Velocity, using the Double Pulsar, to match the CMB dipole velocity of 368 km/s with 99.8% precision.
Why don't scientists engage with me and support the right of my theory to be part of the discussion? It is overdue.
Re. "What is the apparent value of the cosmological constant?", the value inferred from astronomical observations (e.g. of Type Ia supernovae) is in fact Λ ~ 2 H_0^2, where H_0 is the present Hubble expansion rate. This is ~70 km/s/Mpc - corresponding to a minuscule ~10^{-42} GeV in particle physics units - so is neither a constant nor has any connection to quantum field theory. It does however enter into every cosmological observation and is the only dimensionful quantity in the standard (FLRW) analysis framework ... so naturally sets the scale of Λ. Since the fraction of the critical energy density it makes up is \Omega_Λ = Λ/3 H_0^2, this is then as high as ~2/3 i.e. Λ becomes the dominant component of the Universe!
It should be clear from the above however that it has nothing to do with quantum field theory. We have known since Pauli's 1933 remark that "as is obvious from experience, the [zero-point energy] does not produce any gravitational field” - otherwise we would not be here today billions of years after the Big Bang, in a slowly expanding universe. It should have either recollapsed or gone into exponentially rapid expansion without end when the temperature dropped to around ~100 GeV (if not earlier) and the Standard Model vacuum energy began to dominate. As you say, the mystery of *why* it does not gravitate remains unsolved to this day ... but to completely ignore this huge embarrassment and nevertheless invoke a tiny Λ to explain the inferred cosmic acceleration in the ΛCDM model makes no sense at all!
First, it is true that observationally the inferred cosmological constant is of order
\Lambda \sim H_0^2, or equivalently that the associated ''vacuum energy'' density is
\rho_\Lambda \sim M_{\rm Pl}^2 H_0^2. This is because the accelerated expansion becomes dynamically relevant today, hence the inferred scale must be comparable to the present time critical density. That does not mean however that \Lambda is ''not a constant'' or that it is disconnected from quantum field theory. In GR \Lambda is literally a constant in the Einstein equations, and in the effective field theory it is precisely the term that receives contributions from all vacuum energies, the particle condensates, phase transitions (I discuss below), and remnant inflationary radiative corrections, but the latter refer to the primordial era.
Pauli's remark is historically important of course, but only historically. It was made before modern renormalized quantum field theory, and quantum field theory in curved spacetime existed. Today the situation is better understood, naive zero-point estimates are not physical observables by themselves, because the vacuum energy is renormalized. However, after the renormalization there still remain enormous naturalness problems, since known contributions from electroweak symmetry breaking, the QCD condensates, and other sectors are vastly larger than the observed value.
Actually, vacuum energy gravitates because gravity couples to the stress-energy tensor and the Lorentz-invariant vacuum has a stress energy contribution,
which is mathematically identical to a cosmological constant. The problem is instead why the enormous quantum contributions apparently cancel almost exactly, leaving behind only the residual tiny observed value cosmologically. That is the cosmological constant problem.
To this end, as in the above, the vacuum energy in GR is basically realized by a scalar field, so the vacuum energy of a primordial scalar field, the inflaton, basically inflated the Universe and its vacuum oscillations reheated the Universe post-inflationary. The true vacuum in the inflaton sector is the minimum around which the inflaton oscillated and reheated the Universe. There is another known vacuum, the Higgs vacuum, which dominated the Universe after the 100GeV, the Higgs vacuum, when the Universe's temperature dropped around 100Gev. However, this is an assumption, we know we have mass, the Higgs is also massive, but we have no idea of what the electroweak phase transition is, first, second order, did the Higgs vacuum penetrated to the new vacuum, or did it fast rolled or slow-rolled to the new vacuum? So you see there are more vacua than the simple vacuum energy you refer to. It is a simplistic approach discussing vaguely about the ''vacuum energy''
There are many more things to know about the Higgs vacuum, and even some late-time phase transitions triggered by ALPs or other light particles which they also can generate a new vacuum of the theory. Perhaps the inflaton can be the axion, or even the Higgs. Once inflation is confirmed observationally, we may start concrete discussions on this topic.
So it is puzzling, indeed a puzzling topic, but it is an overstatement to state that ''huge embarrassment and nevertheless invoke a tiny Λ to explain the inferred cosmic acceleration in the ΛCDM model makes no sense at all''
Nobody is embarrassed if the puzzle picks are laid correctly on the table. We mainly have two problems, what drove inflation (CMB S4/Simons will answer), what drives late-times (DESI is working on it), are phase transitions invoked (LISA can answer probably), how many vacua are involved and so on. So many problems exist, but the lack of answers is not embarrassing.
One could say the same for black holes before 10 years, nobody confirmed their presence back then until 2019. We are working on problems as a community. Stating ''huge embarrassment'' for the cosmological constant problem is condescending and rather biased towards other solutions, like peculiar velocities, which are openly discredited by experts in GR.
The ΛCDM explains:
Type Ia supernova distances,
the CMB angular power spectrum,
BAO measurements,
structure formation,
and the late-time expansion history,
with a single additional parameter. The theoretical naturalness problem is severe, but that does not invalidate the observational successes of the model.
Finally, you are mentioning the SM as a complete model. It's not. The neutrino is there, it has mass, right handed neutrinos must be present either in Dirac or Majorana terms, or even sterile neutrino forms. And intriguingly, the fourth power of the neutrino mass, yields approximately the present day vacuum energy.
I explained the Pantheon Supernova Observations using my epoch-dependent G model. The model has just two parameters: the 4D radius of the Universe and the G**(-alpha) dependence of the Absolute Luminosity of SN1a. I derived that to be alpha=3.0. That makes all photometric distances to be overestimated by G**(1.5). In HU G= G0 * (1+z) so, all distances are overestimated by (1+z)**1.5
Once you correct the distances, HU predicts the photometric distance with D(z) = R0 * z/(1+z)
where R0 = 14.5 GLY and H0 = 67.5 km/s/Mpc
That matches the CMB H0 and thus there is no Crisis In Cosmology left.
Of course, I also refuted NASA Laser Lunar Ranging analysis and SN1a based G-variability papers. They are of poor quality and made basic mistakes. SN1a papers keep the Stellar Candles Hypothesis (which is the same as the constant G hypothesis) and try to ascertain G variability. NASA has used the G-Constant determined Earth moment of inertia when trying to evaluate G-variability.
Those are basic mistakes.
Earth Temperature History was explained by having the Sun being born as a binary (0.3:0.7). The initial mass distribution was defined by the early Earth Temperature. The time of merger was defined by the current core isotope composition. I modified MESA code to accommodate variable G. When the Sun was born, G was 1.47 G0 (where G0 is the current value of G).
In other words, I created a better model than L-CDM (1 parameter instead of seven), debunked constraints on G variability. The only problem I have is that journal editors will simply reject my work without providing a single reason or a peer review.
Of course, my work also predicted all planets' and binary pulsars' precession and derived the SSB Reference Frame Absolute Velocity, using the Double Pulsar, to match the CMB dipole velocity of 368 km/s with 99.8% precision.
Why don't scientists engage with me and support the right of my theory to be part of the discussion? It is overdue.
Re. "What is the apparent value of the cosmological constant?", the value inferred from astronomical observations (e.g. of Type Ia supernovae) is in fact Λ ~ 2 H_0^2, where H_0 is the present Hubble expansion rate. This is ~70 km/s/Mpc - corresponding to a minuscule ~10^{-42} GeV in particle physics units - so is neither a constant nor has any connection to quantum field theory. It does however enter into every cosmological observation and is the only dimensionful quantity in the standard (FLRW) analysis framework ... so naturally sets the scale of Λ. Since the fraction of the critical energy density it makes up is \Omega_Λ = Λ/3 H_0^2, this is then as high as ~2/3 i.e. Λ becomes the dominant component of the Universe!
It should be clear from the above however that it has nothing to do with quantum field theory. We have known since Pauli's 1933 remark that "as is obvious from experience, the [zero-point energy] does not produce any gravitational field” - otherwise we would not be here today billions of years after the Big Bang, in a slowly expanding universe. It should have either recollapsed or gone into exponentially rapid expansion without end when the temperature dropped to around ~100 GeV (if not earlier) and the Standard Model vacuum energy began to dominate. As you say, the mystery of *why* it does not gravitate remains unsolved to this day ... but to completely ignore this huge embarrassment and nevertheless invoke a tiny Λ to explain the inferred cosmic acceleration in the ΛCDM model makes no sense at all!
Interesting approach but conflated.
First, it is true that observationally the inferred cosmological constant is of order
\Lambda \sim H_0^2, or equivalently that the associated ''vacuum energy'' density is
\rho_\Lambda \sim M_{\rm Pl}^2 H_0^2. This is because the accelerated expansion becomes dynamically relevant today, hence the inferred scale must be comparable to the present time critical density. That does not mean however that \Lambda is ''not a constant'' or that it is disconnected from quantum field theory. In GR \Lambda is literally a constant in the Einstein equations, and in the effective field theory it is precisely the term that receives contributions from all vacuum energies, the particle condensates, phase transitions (I discuss below), and remnant inflationary radiative corrections, but the latter refer to the primordial era.
Pauli's remark is historically important of course, but only historically. It was made before modern renormalized quantum field theory, and quantum field theory in curved spacetime existed. Today the situation is better understood, naive zero-point estimates are not physical observables by themselves, because the vacuum energy is renormalized. However, after the renormalization there still remain enormous naturalness problems, since known contributions from electroweak symmetry breaking, the QCD condensates, and other sectors are vastly larger than the observed value.
Actually, vacuum energy gravitates because gravity couples to the stress-energy tensor and the Lorentz-invariant vacuum has a stress energy contribution,
T_{\mu\nu}^{\rm vac} = -\rho_{\rm vac} g_{\mu\nu},
which is mathematically identical to a cosmological constant. The problem is instead why the enormous quantum contributions apparently cancel almost exactly, leaving behind only the residual tiny observed value cosmologically. That is the cosmological constant problem.
To this end, as in the above, the vacuum energy in GR is basically realized by a scalar field, so the vacuum energy of a primordial scalar field, the inflaton, basically inflated the Universe and its vacuum oscillations reheated the Universe post-inflationary. The true vacuum in the inflaton sector is the minimum around which the inflaton oscillated and reheated the Universe. There is another known vacuum, the Higgs vacuum, which dominated the Universe after the 100GeV, the Higgs vacuum, when the Universe's temperature dropped around 100Gev. However, this is an assumption, we know we have mass, the Higgs is also massive, but we have no idea of what the electroweak phase transition is, first, second order, did the Higgs vacuum penetrated to the new vacuum, or did it fast rolled or slow-rolled to the new vacuum? So you see there are more vacua than the simple vacuum energy you refer to. It is a simplistic approach discussing vaguely about the ''vacuum energy''
There are many more things to know about the Higgs vacuum, and even some late-time phase transitions triggered by ALPs or other light particles which they also can generate a new vacuum of the theory. Perhaps the inflaton can be the axion, or even the Higgs. Once inflation is confirmed observationally, we may start concrete discussions on this topic.
So it is puzzling, indeed a puzzling topic, but it is an overstatement to state that ''huge embarrassment and nevertheless invoke a tiny Λ to explain the inferred cosmic acceleration in the ΛCDM model makes no sense at all''
Nobody is embarrassed if the puzzle picks are laid correctly on the table. We mainly have two problems, what drove inflation (CMB S4/Simons will answer), what drives late-times (DESI is working on it), are phase transitions invoked (LISA can answer probably), how many vacua are involved and so on. So many problems exist, but the lack of answers is not embarrassing.
One could say the same for black holes before 10 years, nobody confirmed their presence back then until 2019. We are working on problems as a community. Stating ''huge embarrassment'' for the cosmological constant problem is condescending and rather biased towards other solutions, like peculiar velocities, which are openly discredited by experts in GR.
The ΛCDM explains:
Type Ia supernova distances,
the CMB angular power spectrum,
BAO measurements,
structure formation,
and the late-time expansion history,
with a single additional parameter. The theoretical naturalness problem is severe, but that does not invalidate the observational successes of the model.
Finally, you are mentioning the SM as a complete model. It's not. The neutrino is there, it has mass, right handed neutrinos must be present either in Dirac or Majorana terms, or even sterile neutrino forms. And intriguingly, the fourth power of the neutrino mass, yields approximately the present day vacuum energy.