Had Tsarist Russia had more competent leadership in the early 20th century and thus would have been able to get through WWI without enduring a revolution, could we eventually see a Tsarist-U.S. Cold War develop?
Or would Tsarist Russia have been uninterested in a struggle for global influence with the U.S. in this TL?
(Also, please keep in mind that a victorious Tsarist Russia will have no immediate enemies in continental Europe; indeed, Germany would be crushed, France would still be its ally, and Britain isn't actually on the European mainland.)
I am quite doubtful that Tsarist Russia would be a rival to the US in the 20th Century. The odds are that had the Tsars remained in power, Russia would look like a large Latin American state with a population of 800 million (mostly poor people). That would be enough to make them a great power, but it would not allow them to even pretend to be a superpower as they did OTL (no doubt about it, the Soviets were pretending - the Soviets were at no point an equal to the US in economic or military power).
(Of course, such a Tsarist Russia could emerge as the superpower rival to China in TTL's 21st Century - so a slower path, but also maybe a more sustainable one than was taken OTL.)
To be able to reach superpower status in the 20th Century, Russia needed radical economic policies, which likely means radical political parties who can't work with a Tsar (since the Tsar was linked to the nobility and the nobility would oppose the radical land reform any serious Russian reformers would need to implement).
The best way to get a non-Soviet 20th Century superpower Russia is probably a Russian republic that hung on to the end of WW1 and was controlled by moderate socialists and Social Revolutionaries (in other words, a government who governed in the interests of the cities and the peasants).
Wouldn't the ideological difference be autocracy vs. freedom?
So the US is upset at Russian autocracy, but in TTL, France, birthplace of Freedom (tm), is not?
I think it would be more likely that the US and Russia would continue to be friendly (both have good reasons to be wary of British power and neither have interests that clash much). By contrast, France may not be a Russian ally for long (in OTL the Franco-Russian Entente was fraying badly due to French distaste at Tsarism before WW1 happened), particularly if Germany is seen to be cut down to size.
To get a cold war between Russia and America, one really needs an ideology that has enough universal appeal that the US would feel threatened by it.
I'm not sure what could alarm the US as much as the atheist working-class violence of Bolshevism (which hit alot of the hot buttons of the time).
EDIT: OK... Maybe a Cold War could happen due to non-ideological competition to claim Europe as a sphere of influence. Such a cold war would require a MUCH stronger Russia though. The Soviet Union was able to use Socialism in OTL to really make itself seem much more influential than it was.
fasquardon