# If the energy density during inflation were lower, how would the CMB look in comparison to the observed CMB today?

I am assuming that a big bang followed by inflation is still theoretically possible with a different starting density. Would the CMB look the same but just colder?

• By "less mass" Do you mean "if the density of the universe was less than the critical density". Observations suggest that the density is equal to the critical density (to within the accuracy of the observations) If the density is less then the universe is open and expands forever. May 30, 2023 at 9:28
• @James K I just meant that if the inflation potential energy created photons quarks leptons etc of a total mass less than the total mass of those particles when the present universe started out, would the CMB have a physically different shape on a plot or would it just look colder? I think this is ultimately about how does the inflaton develop when it starts with with less potential energy.
– user50918
May 30, 2023 at 9:43
• Then again, most (70%?) of the mass/energy budget of the universe is dark energy, and apparently not "particles" at all, and only a small amount of the mass is "photons, quarks, leptons" Most of the mass-in-the-form-of-matter is "etc" (ie dark matter) May 30, 2023 at 9:59
• Dark energy doesn't affect the inflation period when particles were being created. The amount of DE grew with time
– user50918
May 30, 2023 at 10:11
• @Sten Yes the energy density of the entire universe as inflation began
– user50918
May 30, 2023 at 13:02

We don't know the energy density during inflation. This should immediately tell you that it doesn't (directly) impact any of the observables that we are able to measure.

Even though the inflation energy density sets the "initial temperature" of the Universe, the known processes that give rise to today's Universe, like nucleosynthesis and recombination, are connected to the temperature of the Universe and not the time. That is, they occur at a set temperature, irrespective of what the initial temperature was. For example, the temperature at which the cosmic microwave background (CMB) last scattered is set by atomic physics: it's the temperature at which neutral hydrogen atoms become thermodynamically favored over free protons and electrons. By the way, this temperature doesn't even affect the overall CMB temperature today; it only affects the temperature variations.

There are also unknown processes responsible for

• the abundance of an asymmetric component of ordinary matter (more matter than antimatter);
• the abundance of dark matter;
• the initial variations in the density of the Universe;
• the abundance of dark energy.

The outcomes of these processes affect the temperature variations in the CMB. It's possible that these outcomes depend on the inflation energy density (e.g. if both the matter and the radiation were decay products of the inflaton field), but any claim to this effect would depend on the particular speculative model of baryogenesis, dark matter, inflation, or dark energy that you adopt.

• I think the temperature just depends on the photon/baryon ratio and $\Omega_bh^2$ right? May 31, 2023 at 9:47
• @ProfRob i.e. the photon density today, yes. But I'm aiming at the more general question of what the CMB looks like (not just the monopole), which depends on many more cosmological parameters.
– Sten
May 31, 2023 at 11:19