Modern cosmology

Содержание и основные понятия

The cosmological model combines space expansion, relic radiation, light element formation and structure development; its parameters are specified by independent observations.
GEF · 11 grade
PIF · Baseline
Interactive model
Big Bang
Relict radiation
dark matter
dark energy
horizon
01
The physical picture
What happens and what boundaries the model has.
Main message
The cosmological model combines space expansion, relic radiation, light element formation and structure development; its parameters are specified by independent observations.
The red shift of distant galaxies is growing at an average distance.
Dark matter is detected by gravitational action, dark energy by accelerated expansion.
The observed universe is limited to the final time of light spreading, not to the material wall.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
v
=
H
0
d
v=H_0d
v
=
H
0
​
d
Hubble Law for Small Distances
z
=
λ
наб
−
λ
0
λ
0
z=\frac{\lambda_{\text{наб}}-\lambda_0}{\lambda_0}
z
=
λ
0
​
λ
(Signed) Nab
​
−
λ
0
​
​
Cosmological red displacement
Review of the situation
The further the object, the more early we see the universe, because its light has been coming to us for billions of years.
04
Links and application
In the real world
The further the object, the more early we see the universe, because its light has been coming to us for billions of years.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Contemporary cosmology" through a model, not just a formula.
Outcome 2
Distinguish and correctly use terms: Big Bang, Relic Radiation, Dark Matter.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Big Bang
A cosmological model of the evolution of the universe from an early hot and dense state.
Relict radiation
Space microwave background radiation, preserved from the hot early universe.
dark matter
Observed by gravitational action of matter that does not emit detected electromagnetic radiation.
dark energy
Name of the component of the cosmological model associated with the accelerated expansion of the universe.
horizon
The boundary of an area from which an observer can reach the signal; the meaning is specified by a specific cosmological model.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
v
=
H
0
d
v=H_0d
v
=
H
0
​
d
empirical law
The law of the habble for small distances.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
z
=
λ
наб
−
λ
0
λ
0
z=\frac{\lambda_{\text{наб}}-\lambda_0}{\lambda_0}
z
=
λ
0
​
λ
(Signed) Nab
​
−
λ
0
​
​
The displacement of the spectral lines of the galaxy measures red displacement.
v
≈
c
z
v\approx cz
v
≈
cz
In the case of small z, the red displacement is equivalent to the removal rate.
v
∝
d
⇒
v
=
H
0
d
v\propto d\quad\Rightarrow\quad v=H_0d
v
∝
d
⇒
v
=
H
0
​
d
Observations show approximately linear growth in speed with distance; the inclination factor is constant to Hubble.
Conditions:
Small cosmological red shifts, where v eu cz is long enough for pecular speeds to be small, but relativist cosmology has not yet required a non-linear connection.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
z
=
λ
наб
−
λ
0
λ
0
z=\frac{\lambda_{\text{наб}}-\lambda_0}{\lambda_0}
z
=
λ
0
​
λ
(Signed) Nab
​
−
λ
0
​
​
definition
Cosmological red shift.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
λ
0
\lambda_0
λ
0
​
The lab length of the spectrum line sets the standard without cosmological extension.
Δ
λ
=
λ
наб
−
λ
0
\Delta\lambda=\lambda_{\text{наб}}-\lambda_0
Δ
λ
=
λ
(Signed) Nab
​
−
λ
0
​
The change of line is equal to the difference between the observed and reference wave lengths.
z
:
=
Δ
λ
λ
0
z:=\frac{\Delta\lambda}{\lambda_0}
z
:=
λ
0
​
Δ
λ
​
The reference length divide gives an unlimited measure of red displacement.
Conditions:
The same spectral line is well identified; . . above and .0 are measured in the same units. For cosmological extension 1 + z = a0/aam.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't move the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that the red shift of remote galaxies increases on average with distance.
How to Check the Mind
Dark matter is detected by gravitational action, dark energy by accelerated expansion. Then check the unit, vector direction and result behaviour at zero or very large parameter.
Σ
Conclusion on the topic
Modern cosmology
The cosmological model combines space expansion, relic radiation, light element formation and structure development; its parameters are specified by independent observations.
The red shift of distant galaxies is growing at an average distance.
Dark matter is detected by gravitational action, dark energy by accelerated expansion.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.